Let sinx= -3/5,where 3π/2≤x≤ 2π , and cosy= -5/13,whereπ ≤x≤ 3π/2. Find the exact value of

a) cos2x

b) cos(y/2)

c) cos(x + y)

d) sin (x - y)

My work:

a) cos2x = 1 - 2sin^2x

for sin x = -3/5 -----> 1-2(-3/5)^2 = 7/25

for cosy = -5/13 -----> 1-2(-12/13)^2 = -119/169

b) cos(y/2) = √(1+ cosy)/2

for cosy = -5/3 -----> √(1+(-5/13))/2 = 2/√13

for siny = -3/5 -----> √(1+(4/5))/2 = 3/(2√5)

c) cos(x + y) = (cosx)(cosy) - (sinx)(siny)

(4/5)(-5/13) - (-3/5)(-12/13)

(-20/65) - (36/65) = -56/65

d) sin(x - y) = (sinx)(cosy) + (cosx)(siny)

(-3/5)(-5/13) + (4/5)(-12/13)

= (-15/65) + (-48/65) = -63/65