# How do you find cos(t) if t is in the 3rd quadrant and tan(t)= 3?

$- \frac{1}{\sqrt{10}}$
First we get cos t value in the first quadrant. For this compute ${\sec}^{2} t = 10$ so that cos t= $\frac{1}{\sqrt{10}}$. In the third quadrant it wouls be cos(t+180)= -cos t= $- \frac{1}{\sqrt{10}}$