Question

Given cos x = -3/5 , sin y =12/13 and 0º< x <360º,x and y are on the same quadrant. Without using mathematical table and scientific calculator,find the values for:
(a)sin 1/2 x
(b)cos (x+y)

Answer 1

since cosx < 0 and siny > 0, and both x and y are in the same quadrants, the angles must be in II

if cosx = -3/5, then sinx = 4/5
if siny = 12/13, then cosy = - 5/13

a) from cos 2A = 1 - 2 cos^2 A
cos x = 1 - 2 sin^2 (x/2)
-3/5 = 1 - 2sin^2 (x/2)
2sin^2 (x/2) = 1 + 3/5 = 8/5
sin^2 (x/2) = 4/5
sin (x/2) = 2/√5

b)
cos(x+y) = cosxcosy - sinxsiny
= sub in the above values and simplify