Find the exact value of the trig function below.

Question

cos2Ø if sinØ = 2/5

Answer 1

from sinØ = 2/5, sketch a right-angled triangle
Use Pythagoras to find cos Ø
cos^2 Ø + sin^2 Ø = 1
cos^2 Ø = 21/25

cos 2Ø = cos^2 Ø - sin^2 Ø, you should know that identity
cos 2Ø = 21/25 - 4/25 = 17/25

Answer 2

cos(2x) = 1 - 2sin^2(x)

now just use your numbers.