Question

given that cos theta=4/5find sin theta

Answer 1

use trig identity
sin^2+cos^2 =1
sin^2 = 1-cos^2
.......
since cos = 4/5
cos^2 = 16/25
1-cos^2 = 1-16/25 = 9/25
.........
sin^2 = 9/25
sin = 3/5

Answer 2

Or you could use a right triangle. Knowing cosine = adj/hyp, you could use pythagorean theorem (a^2 + b^2 = c^2) to find the missing side of the triangle (which would be 3). Then since, sine = opposite/hyp, you would get 3/5