Question

有关三角恒角变化的题目 已知sin(a+π/3)+sina=-4√3/5,-π/2

Answer 1

sin(a+π/3)+sina=-4√3/5

sinacosπ/3+cosasinπ/3+sina=-4√3/5

3/2sina+√3/2cosa=-4√3/5

sina=-(1/√3)cosa-8/(5√3)

代入sina^2+cosa^2=1,可得

100cosa^2+80cosa-11=0

cosa=(-4+3√3)/10或cosa=(-4-3√3)/10

由-π/2