Solve the trigonometry problem

Question

If SinΘ=√17/17, Find cotΘ

Im having trouble finding out how to break down the √17/17, thank you!

Answer 1

You cannot progress from sin(Θ) directly to cot(Θ). You need to find cos(Θ) first and could use your cos²(Θ) + sin²(Θ)=1. Please remember that when you solve for cos(theta) by taking the square root, that you have to select either a + or - as square rooting both sides gives a possibility of a positive or negative. Hopefully, you were given some information regarding the quadrant you are in to select the proper sign. Then you can go to the definition of cot(Θ) = cos(Θ)/sin(Θ).

Did that help? Or would you like some more assistance?

Answer 2

Hi! Sketch the right triangle in Q1 and label the appropriate sides as rad 17 and 17. Then solve for the adjacent side using Pythagorean Theorem. At this point you will know the side lengths needed to give the exact value of cot theta.

** Also, the rad 17 over 17 could be expressed in prerationalized form: 1 over rad 17.