If tan (theta) = 3/4 and theta is an acute angle, find cos (theta)

Sin t / cos t = 3 / 4

4 sin t = 3 cos t

sin t = 3 cos t / 4

sin² t + cos² t = 1

(3 cos t / 4) ² + cos² t = 1

9 cos² t / 16 + cos² t = 1 / · 16

9 cos² t + 16 cos² t = 16

25 cos² t = 16

cos ² t = 16/25

Answer:

cos t = 4 / 5