If tan x = 3/4, find the values of cos x and sin x.
Correct: A
We have tan x = 3/4. By definition, tan x = sin x / cos x. So we have sin x / cos x = 3/4, or sin x = (3/4)cos x. Also, sin^2 x + cos^2 x = 1. Substituting sin x = (3/4)cos x, we get ((3/4)cos x)^2 + cos^2 x = 1, or (9/16)cos^2 x + cos^2 x = 1, or (9/16 + 16/16)cos^2 x = 1, or (25/16)cos^2 x = 1. So cos^2 x = 16/25 and cos x = ±4/5. However, if cos x is negative, then sin x will also be negative, and tan x will be positive. So cos x must be positive. Hence cos x = 4/5 and sin x = (3/4) * (4/5) = 3/5.