# Thread: Exact value of tan (x)

1. ## Exact value of tan (x)

If sec (x) = -4/3 and sin (x) > 0, find the exact value of tan (x)...

2. ## Sec and tan

If sec (x) = -4/3 and sin (x) > 0, find the exact value of tan (x)...
First you need to use:

$\sec^2 x = 1 + \tan^2 x$

This will give you a value for $\tan^2 x$. When you take the square root, be careful with the $\pm$ sign. Which do you choose?

Well, we're told that $\sin x > 0$ and $\sec x < 0$. Now $\cos x = \frac{1}{\sec x}$. So $\cos x < 0$. And, of course, $\tan x = \frac{\sin x}{\cos x}$, so $\tan x < 0$ also.