# Suppose cos(x) = u, how do you write tan(x) in terms of x?

Jul 16, 2016

$\tan \left(x\right) = \frac{\sin \left(x\right)}{\cos \left(x\right)}$

#### Explanation:

Remember from SOH CAH TOA that

$\cos \theta = \left(\text{Adjacent")/("Hypotenuse}\right)$

We can use this to construct a triangle.

From the triangle, we see that

$\tan \left(x\right) = \frac{\sqrt{1 - {u}^{2}}}{u}$

$\tan \left(x\right) = \frac{\sqrt{1 - {\cos}^{2} \left(x\right)}}{\cos \left(x\right)} = \frac{\sqrt{{\sin}^{2} \left(x\right)}}{\cos} \left(x\right)$

$\therefore \tan \left(x\right) = \frac{\sin \left(x\right)}{\cos \left(x\right)}$