1)tan Q = -3/4 Find cosQ

Question

-3^2 + 4^2 = x^2
9+16 = sqrt 25 = 5

cos = ad/hy = -4/5

Am I correct?

2) Use the sum and difference identites

sin[x + pi/4] + sin[x-pi/4] = -1

sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1

2 sin x cos pi/4 =-1

cos pi/4 = sqr2/2

2sin^x(sqrt2/2) = -1
sin x = -sqrt2

x = 7pi/4 and 5pi/4

Am I correct?

Answer 1

-3^2 + 4^2 = x^2
9+16 = sqrt 25 = 5

cos = ad/hy = -4/5

Am I correct?
Yes, but that is only in quadrant 3.
Over in quadrant 4, say x = +4 and y = -3
then cos = 4/5