Trigonometry problem

Question

Given that cotθ=√13/4 and cosθ is positive, determine cosθ. Write the exact answer. Do not round.

Answer 1

Hi Kendra, here's some guidance on how to write the cosine ratio based on the given cotangent ratio.

We know that cot(θ)=(adjacent side length)/(opposite side length). As cot=√(13)/4, we know that the adjacent side has length √(13) and the opposite side has length 4. We also know that cos(θ)=(opposite side length)/(hypotenuse length). We already know the opposite side length, but now need to find the hypotenuse side length. You can find this by using the Pythagorean Theorem to solve for the hypotenuse length (c).

Let me know if you need more help with this problem. I'm happy to help!