I have the following problem:
If $ \cot{C} = \frac{\sqrt{3}}{7} $, find $ \csc{C} $
From my trig identities, I know that $ \cot{\theta} = \frac{1}{\tan{\theta}} $, and $ \csc{\theta} = \frac{1}{\sin{\theta}} $, and also $ \cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} $
However, I can't seem to see how to connect the dots to get from cotangent to cosecant. I figure I might be able to use the last identity if I can somehow make $ \cos{C} = 1 $, but I don't really see how to do that, either.
This is homework, so please provide me with some pointers rather than complete solutions.
Thanks.
Best Answer
In my answer here, I describe some general ideas for how to use one trig function of an angle to determine another trig function of the same angle. The basic idea is to draw triangle(s) on a coordinate system that correspond to the given trig function and use those to compute the other trig function.