The angle t is an acute angle and sin t is given. Use the Pythagorean identity sin^2t+cos^2t=1 to find cos t.

Question

sin t = 2/5

cos t = ____

Answer 1

sin²t + cos²t = 1, sint = 2/5, and t is acute

cos²t = 1 - sin²t

cost = ± √ (1 - sin²t)

Since t is acute, cost > 0.

So, cost = √ (1 - sin²t) = √ (1 - 4/25) = √ (21/25) = √21 / 5