Question

五道高中三角函数数学题,一.已知a是三角形的内角,且sina+cosa=5/1,则tana为多少二.函数y=cos(si

Answer 1

1 sina =2*tan(a/2)]/{1 +[tan(a/2)]^2}

cosa ={1 -[tan(a/2)]^2}/{1 +[tan(a/2)]^2}

代入sina+cosa=1/5,解得:tan(a/2) =2,[tan(a/2) >0]

==> tana =[2*tan(a/2)]/{1 -[tan(a/2)]^2} = -4/3

3.

4.

5.y=cos²x+2sinxcosx+3sin²x

=1+sin(2x)+2sin²x

=sin(2x)+cos(2x)

=√2sin(2x+π/4)

最小正周期Tmin=2π/2=π

当sin(2x+π/4)=-1时,有ymin=-√2

2kπ-π/2≤2x+π/4≤2kπ+π/2 (k∈Z)时,即kπ-3π/8≤x≤kπ+π/8 (k∈Z)时,函数单调递增.

单调递增区间为[kπ-3π/8,kπ+π/8] (k∈Z)

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