# Given sin theta=3/5 and cos theta=4/5, how do you find tan theta?

Jun 10, 2016

$\tan \theta = \frac{3}{4}$

#### Explanation:

Recall the quotient identity $\tan x = \sin \frac{x}{\cos} x$

$\tan \theta = \sin \frac{x}{\cos} x$

$\tan \theta = \frac{\frac{3}{5}}{\frac{4}{5}}$

$\tan \theta = \frac{3}{5} \times \frac{5}{4}$

$\tan \theta = \frac{3}{4}$

Note you could have also said that

$\sin \theta = \text{opposite"/"hypotenuse}$, $\cos \theta = \text{adjacent"/"hypotenuse}$ and $\tan \theta = \text{opposite"/"adjacent}$.

If we know that $\sin \theta = \frac{3}{5}$, the side opposite $\theta$ measures 3.

If we know that $\cos \theta = \frac{4}{5}$, the side adjacent $\theta$ metres 4.

Applying the definition of $\tan \theta = \text{opposite"/"adjacent}$, we have that $\tan \theta = \frac{3}{4}$

Hopefully this helps!