Functions Example

Question:
Given: f(cos x) = cos 2x, find f(sin x) = ?
Solution:
sin x = cos(90o - x)
f(sin x) = f[cos(90o - x)]
= cos 2(90o - x)
= cos(180o - 2x)
= cos180o cos 2x + sin180o sin 2x
= - cos 2x
Rules used in this example:
sin x = cos(90o - x)
cos(x - y) = cos x cos y + sin x sin y
sin180o = 0
cos180 = -1