[新编]高中数学人教A版必修4习题：第一章三角函数1.3.2-可编辑

第2课时　诱导公式五、六

课时过关·能力提升

基础巩固

1已知sin α

A

解析:coα=

答案:C

2已知si

A.-

解析:siα∈sinα=tanα

答案:A

3若sin(3π+α)=

A.

解析:由已知,得sinα

则coα=

答案:A

4化简sin 95°+cos 175°=　　　　　. 

解析:sin95°+cos175°=sin(90°+5°)+cos(180°-5°)=cos5°-cos5°=0.

答案:0

5已知si

解析:∵si

∴si

答案:

6化

解析:原

=

答案:-1

7求证

证明左,故原等式成立.

8已知角α的终边经过点P(-4,3),

解∵角α的终边经过点P(-4,3),

∴tanα

∴原α=

9已知sin α

解∵sinαα=

∴tanα

∴原式=tanα

=tanα

能力提升

1已知si

A

解析:co

=-si

答案:B

2在△ABC中,已知co

A.

解析:∵co,

∴co

答案:C

3若f(sin x)=3-co

A.3+sin x B.3-sin x

C.3-cos x D.3+cos x

解析:∵f(sinx)=3-cox,

∴f(x)=3+x.∴f(cosx)=3+cosx.

答案:D

4若co

解析:∵co

=co

∴si

答案:a

5定义:角θ与φ都是任意角,若满足θ+φ=90°,则称θ与φ“广义互余”.已知sin(π+α)=

①sin β

③tan β

答案:①③

★6sin21°+sin22°+sin23°+…+sin289°=　　　　. 

解析:sin21°+sin22°+sin23°+…+sin289°=(sin21°+sin289°)+(sin22°+sin288°)+…+(sin244°+sin246°)+sin245°=(sin21°+cos21°)+(sin22°+cos22°)+…+(sin244°+cos244°)+sin245°=44

答案:

7已知cos α=

(1)求sin α的值;

(2)求f(α)

解(1)因为cosα=α为第三象限角,

所以sinα=

(2)f(α)

=tanαsinα·sinα

★8若△A1B1C1的三个内角的余弦值分别等于△A2B2C2对应三个内角的正弦值,试借助诱导公式证明△A2B2C2必有一个内角为钝角.

证明由题意可知,

不妨

若A2,B2,C2全为锐角,则

A2+B2+C2.

又A2,B2,C2不可能为直角,且满足A2+B2+C2=π,故必有一个内角为钝角.

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考前的心理准备，考前可通过心理暗示缓解紧张情绪，进行临场心理调节。紧张时可用“我能行”、“静心”、“认真”等自我暗示来稳定情绪，适当做做深呼吸。放松心情，减少压力，参加成考的学生需要将平时的家庭、学校、社会的压力全丢掉，轻装上阵。Coming back home in the evening, family and I sat and watched TV together, we are returning and eating the fruit while chatting, the whole family is happy and harmonious!考试要淡定。拿到试卷后，不要急于动笔，先浏览试题，粗略知道各题的难易、分值后合理安排答题时间。分值较小的题，如果一时做不出来，可先放一放，抢时间先做会做的题，然后再回头考虑本题。.I live very happily today! In the morning, it is very fine! Then I climb the mountain with family, the air on the mountain is very fresh, the flowers plants and trees on the mountain all seem extremely beautiful.

考前的心理准备，考前可通过心理暗示缓解紧张情绪，进行临场心理调节。紧张时可用“我能行”、“静心”、“认真”等自我暗示来稳定情绪，适当做做深呼吸。放松心情，减少压力，参加成考的学生需要将平时的家庭、学校、社会的压力全丢掉，轻装上阵。Coming back home in the evening, family and I sat and watched TV together, we are returning and eating the fruit while chatting, the whole family is happy and harmonious!考试要淡定。拿到试卷后，不要急于动笔，先浏览试题，粗略知道各题的难易、分值后合理安排答题时间。分值较小的题，如果一时做不出来，可先放一放，抢时间先做会做的题，然后再回头考虑本题。.I live very happily today! In the morning, it is very fine! Then I climb the mountain with family, the air on the mountain is very fresh, the flowers plants and trees on the mountain all seem extremely beautiful.

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