- #1

Euler2718

- 90

- 3

1. Homework Statement

1. Homework Statement

*For the following given trigonometric ratio and domain, determine the missing trigonometric ratio.*

## Homework Equations

[tex] cos\theta = -\frac{1}{2} , \frac{\pi}{2}\leq \theta < \pi [/tex] find [tex]cot\theta[/tex]

## The Attempt at a Solution

I know how to do these normally, it's just the "find other trig. ratio" tacked on the end that's sort of distorting me. My attempt was finding the reference angle of the trig. value which turned out to be...

[tex] \theta_{r} = \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} [/tex]

Now, the question is looking for cotangents. Because the original (cosine) was negative, I postulate that you would be looking for negative cotangents in the restriction given (not negative angles, but negative relative to the quadrant). Thus in quadrant two, the answer would be

[tex] \pi - \frac{\pi}{3} = \frac{2\pi}{3} [/tex]

Thank you for reading.