Question

If sinθ = 12/13 and θ is an acute angle, find cotθ.

Answer 1

Answer:

cot(θ)=5/12

Step-by-step explanation:

(I'm going to replace theta with x to save time.)

Recall that sine is equal to opposite over hypotenuse. Thus:

sin(x)=12/13, this means that the opposite side is 12 while the hypotenuse is 13 (well, it doesn't have to be, but their ratios are).

Find the adjacent side using the Pythagorean Theorem.

13^2 = 12^2 + adj^2

adj^2 = 25

adj = 5.

Recall that tan(x) is opposite over adjacent. This means that cot(x) is adjacent is opposite.

Therefore: cot(x) = 5/12.