Question

已知向量a=(4,5cosa),b=(3,--4tana) (1)若a//b,试求sina的值 (2)若a⊥b,且a属于

Answer 1

1)若a//b,则

15cosa=-16tana=-16sina/cosa

15cos^2a+16sina=0

15(1-sin^2a)+16sina=0

15sin^2a-16sina-15=0

sina=-3/5,sina=5/3(舍）

sina=-3/5

2)若a⊥b,则

12-20cosa*tana=0

sina=3/5

a属于(0,π/2),

cosa=1-sin^2a=4/5

cos2a=1-2sin^2a=7/25

sin2a=2sinacosa=24/25

cos（2a-π/4）=cos2acosπ/4+sin2asinπ/4

=(7/25)(√2/2)+(24/25)(√2/2)

=31√2/50