## Bleck3 2 years ago Find cot θ if csc θ = -sqrt37/6 and tan θ > 0.

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1. Bleck3

options are 1/6 sqrt37/37 sqrt37 6

2. Bleck3

@crater9909 any ideas?

3. crater9909

1/6 I'm not sure

4. AnimalAin

Think about the triangle required to get the numbers given. If the csc theta is -sqrt(37)/6, the unscaled triangle is a 1/6/sqrt(37) triangle. Then cot theta will be 1/6 (same sign as tan).

5. AnimalAin

Another way to think about it.$\csc \theta = -\frac{\sqrt{37}}{6} \implies \sin \theta =-\frac{6}{\sqrt{37}} \implies \cos \theta= \pm \frac{1}{\sqrt{37}}$Since tan theta and cot theta are reciprocals, they have to have the same sign. That means$\cot \theta = \frac{1}{6}$