# Finding the other trig. functions with given values

If $\sec\theta = \frac{5}{2}$ and $\csc\theta < 0$, find the other five trig. functions

The "$\csc < 0$" is confusing me. How do I know which quadrant that is in? What if it was "$\cot < 0$"?

• I transcribed the text from the image (despite the very nice handwriting). Please double-check that I got it right.
– Blue
Dec 5, 2013 at 4:03

Definition of $\csc$ is really $\frac{1}{\sin}$ and so if this has to be negative,we are in the third or fourth quadrant. Since the $\sec$ $(=$reciprocal cosine$)$ is positive, we end up in the fourth quadrant, from which the signs of all trig functions are known. Can you further work it out?