Question

已知θ为第二象限角,25sin平方θ+sinθ-24=0,则cosθ/2的值为”

Answer 1

25sin平方θ+sinθ-24=0

(25sinθ-24)(sinθ+1)=0

sinθ=24/25或者sinθ=-1(不合题意舍去因为θ为第二象限角)

cosθ=-[1-(24/25)*(24/25)]^(1/2)=-7/25

2cos(θ/2)*cos(θ/2)-1=-7/25

cos(θ/2)*cos(θ/2)=9/25

所以cos(θ/2)=3/5或-3/5