1.If tan theta=3/4 and theta is an acute angle, find cos theta.

Question

2.If sin theta=12/13 and theta is an acute angle, find cot theta.

Answer 1

Both are done the same way, I will do the first, you do the second

tanØ = 3/4 and Ø is acute, thus in the first quadrant

sketch a right-angled triangle, with Ø at the origin , opposite side = 3 and adjacent side = 4
let the hypotenuse be r
r^2 = 4^2 + 3^2 = 25
r = √25 = 5

now you can find any of the 5 remaining trig ratios.
You want cosØ
cosØ = adjacent/hypotenuse = 4/5