2024届高考数学一轮复习第三篇三角函数、解三角形第2节同角三角函数的基本关系与诱导公式训练理新人教版

The Union Jack was the name of the flag made when England,Scotland and Ireland joined together to make one country.

2024届高考数学一轮复习第三篇三角函数、解三角形第2节同角三角函数的基本关系与诱导公式训练理新人教版

【选题明细表】

知识点、方法 同角三角函数的基本关系式 诱导公式 综合应用问题 题号 1,2,6,11,12,14 7,9,10 3,4,5,8,13 基础巩固(时间:30分钟)

1.(2017·江西模拟)已知sin α=-,且α是第三象限的角,则tan α的值为( A )(A) (B)- (C) (D)-

解析:因为sin α=-,且α是第三象限的角,所以cos α=-=-,则tan α==,故选A.

2.(2017·乐东县一模)已知tan α=3,则等于( B )(A) (B) (C) (D)2 解析:因为tan α=3,所以===.

Sailors used to speak of a “jack” when they meant a flag which was set near the bow of a sailing ship.The flag showed the country to which the ship belonged.The Union Jack became the flag of Great Britain.

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The Union Jack was the name of the flag made when England,Scotland and Ireland joined together to make one country.

故选B.

3.(2017·晋中一模)若sin(π-α)=,且≤α≤π,则cos α等于( B )

(A) (B)- (C)- (D)

解析:因为sin(π-α)=sin α=,且≤α≤π,则cos α=-=-.故选B.

4.(2017·九江一模)已知tan θ=3,则cos(+2θ)等于( C )(A)- (B)- (C) (D) 解析:因为====.故选C.

5.(2017·焦作二模)若cos(-α)等于,则cos(π-2α)等于( D )(A) (B) (C)- (D)-

解析:由cos(-α)=,可得sin α=.

tan θ

=3,则

cos(+2θ

)=sin 2θ

因为cos(π-2α)=-cos 2α=-(1-2sin2α)=2sin2α-1=2×-1=-. 故选D.

Sailors used to speak of a “jack” when they meant a flag which was set near the bow of a sailing ship.The flag showed the country to which the ship belonged.The Union Jack became the flag of Great Britain.2 / 7

The Union Jack was the name of the flag made when England,Scotland and Ireland joined together to make one country.

6.已知-<α<0,sin α+cos α=,则的值为( C )(A) (B) (C) (D)

解析:法一 联立

由①得,sin α=-cos α,将其代入②, 整理得25cos2α-5cos α-12=0.

因为-<α<0,所以

于是==.故选C.

法二 因为sin α+cos α=,

所以(sin α+cos α)2= ()2,可得2sin αcos α=-.

而(cos α-sin α)2=sin2α-2sin αcos α+cos2α=1+=,又-<α<0,所以sin α<0,cos α>0,所以cos α-sin α=. 于是==.故选C.

7.(2017·四川乐山二模)设函数f(x)(x∈R)满足f(x-π)=f(x)+sin x,当0≤x≤π,f(x)=1时,则f(-)等于( C )(A) (B)- (C) (D)-

解析:因为f(x-π)=f(x)+sin x,当0≤x≤π,f(x)=1时,

Sailors used to speak of a “jack” when they meant a flag which was set near the bow of a sailing ship.The flag showed the country to which the ship belonged.The Union Jack became the flag of Great Britain.

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