Question

若cosa=2/3,a是第四象限角，则sin（a—2π）+sin（—a—3π）cos（a—3π）=

Answer 1

若cosa=2/3,a是第四象限角
sina = -√(1 - cos²a) = -√5/3
sin(a - 2π) + sin(-a - 3π)cos(a - 3π)
= -sin(2π - a) - sin(3π+ a)cos(3π - a)
= sina - (-sina)*(-cosa)
= sina - sina*cosa
= sina(1- cosa)
= -√5/3(1-2/3)
= -√5/3 × 1/3
= -√5/9
希望能帮到你O(∩_∩)O

Answer 2

sina = -√(1 - cos²a) = -√5/3
sin(a - 2π) + sin(-a - 3π)cos(a - 3π)
= -sin(2π - a) - sin(2π + π + a)cos(2π + π - a)
= sina - sin(π + a)cos(π - a)
= sina + sinacosa
= sina(1 + cosa)
= -√5/3(1 + 2/3)
= -√5/3 × 5/3
= -5√5/9

Answer 3

sin（a—2π）+sin（—a—3π）cos（a—3π）化简为关于sina和cosa的式子，根据sina^2+cosa^2=1,(sina为负数)，最终计算出结果。