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【323423】2023九年级数学上册 第4章 锐角三角函数4.1 正弦和余弦第1课时 正弦及30°角

时间:2025-01-16 18:33:18 作者: 字数:3619字
简介:


4 锐角三角函数

4.1 正弦和余弦

1课时 正弦及30°角的正弦值

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

要点感知1 在直角三角形中,锐角α________的比叫作角α的正弦,记作sinα,即sinα=____.

预习练习1-1 把△ABC三边的长度都扩大为原来的3倍,则锐角A的正弦值 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> ( )


 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> A.不变 B.缩小为原来的 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C.扩大为原来的3 D.不能确定

1-2 如图,在△ABC中,∠C=90°AB=13BC=5,则sinA的值是( )

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

要点感知2 sin30°=____.

预习练习2-1 计算:sin30°-|-2|=____.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

知识点1 正弦的定义及简单运用

1.(温州中考)如图,在△ABC中,∠C=90°AB=5BC=3,则sinA的值是( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

2.(贵阳中考)Rt△ABC中,∠C=90°AC=12BC=5,则sinA的值为( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

3.正方形网格中,∠AOB如图放置,则sin∠AOB=( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D.2

4.Rt△ABC中,∠C=90°BC=2sinA= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> ,则边AC的长是( )

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B.3 C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

5.已知△ABC中,AC=4BC=3AB=5,则s <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> inA=( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

  1. 如图,在平面直角坐标系内一点P(512),那么OPx轴的夹角α的正弦值是____.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

7.根据图中数据,求sinCsinB的值.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>



知识点2 30°角的正弦值

  1. 如图,孔明同学背着一桶水,从山脚A出发,沿与地面成30°角的山坡向上走,送水到山上因今年春季受旱缺水的王奶奶家(B)AB=80米,则孔明从AB上升的高度BC____.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>


 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> 9.Rt△ABC中,∠C=90°,若AC=2BC,则sinA的值是( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B.2 C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

10.在平面直角坐标系xOy中,已知点A(21)B(30),则sin∠AOB的值等于( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

11.(威海中考)如图,在下列网格 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> 中,小正方形的边长均为1,点ABO都在格点上,则∠AOB的正弦值是( )

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> 12.(怀化中考)如图,小明爬一土坡,他从A处爬到B处所走的直线距离AB=4米,此时,他离地面高度为h=2米,则这个土坡的坡角为____.

13.Rt△ABC中,∠C=90°s <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> inB= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> ,则 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> =____.

14.如图所示,在Rt△ABC中,∠ACB=90°CD⊥ABD为垂足,若AC=4BC=3,求sin∠ACD的值.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>



15.如图,将一张矩形纸片ABCD沿CE折叠,B点恰好落在AD边上的F点,若AB∶BC=4∶5,求sin∠CFD.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>




16.如图所示,△ABC中,∠C=90°sinA= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> AC=2,求ABBC的长.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>




挑战自我

17.(眉山中考)在矩形ABCD中,DC=23CF⊥BD分别交BDAD于点EF,连接BF.

(1)求证:△DEC∽△FDC

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>


  1. FAD的中点时,求sin∠FBD的值及BC的长度.



参考答案

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

要点感知1 对边 斜边 ∠α的对边:斜边

预习练习1-1 A

1-2 A

要点感 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>2  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

预习练习2-1 - <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

1.C 2.D 3.B 4.A 5.A 6. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> 7.Rt△ABC中,BC=34,∴sinC= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> sinB=ACBC=33434. 8.40

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>

  1. C 10.A 11.D 12.30° 13.45 14.∵Rt△ABC中,∠ACB=90°CD⊥ABD为垂足,AC=4BC=3,∴A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> B=5.根据同角的余角相等,得∠ACD=∠B.∴sin∠ACD=sin∠B= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .

  1. 由折叠可知,CB=CF.矩形ABCD中,AB= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> CDsin∠CFD= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .

  2. sinA=13,∴AB=3BC.∵AC2+BC2=AB2,∴22+BC2=(3BC)2,解 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a>BC= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .∴AB= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .

17.(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> 证明:∵矩形ABCD,CF⊥BD,∠ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> DEC=∠FDC=90°,又∠DCE=∠FCD,∴△DEC∽△FDC.(2)∵FAD的中点,AD∥BC,∴FB=FC,∴sin∠FBD= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .EF=x,则FC=3x,CE=2x.∵△DEC∽△FDC,得x=2.∴CF= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .Rt△CFD中,DF= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> ,∴BC=2DF=2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/942/" title="正弦" class="c1" target="_blank">正弦</a> <a href="/tags/943/" title="余弦" class="c1" target="_blank">余弦</a> <a href="/tags/944/" title="三角函数" class="c1" target="_blank">三角函数</a> .

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