If Sin32=t, express each of the following in terms of t.

Question

1.Sin212
2.Cos58
3.Sin16

Answer 1

1. 212 = 180 + 32
sin 212 = -sin32 = -t

2. cos 59 = sin32 = t , complementary angles

3. cos 2A = 1 - 2sin^2 A
cos 32 = 1 - 2sin^2 16
2sin^2 16 = 1 - cos32
sin^2 16 = (1 - cos32)/2
sin 16 = √(1 - cos32) / √2
but cos32 = √1 - sin^2 32) = √(1 - t^2)

son 16 = √ (1 - √(1-t^2) ) / √2