# How do you find the other trigonometric functions given sinx=3/5, cosx=4/5?

Feb 1, 2018

$\tan x = \frac{3}{4}$, $\csc x = \frac{5}{3}$, $\sec x = \frac{5}{4}$, $\cot x = \frac{4}{3}$

#### Explanation:

Since both sine and cosine are positive, we know $x$ is in $Q I$, so all of the trig functions will be positive.

We can use the fact that $\tan x = \sin \frac{x}{\cos} x$ to find tangent:

$\tan x = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}$.

The other functions can be found with the reciprocal identities:

$\csc x = \frac{1}{\sin} x = \frac{5}{3}$
$\sec x = \frac{1}{\cos} x = \frac{5}{4}$
$\cot x = \frac{1}{\tan} x = \frac{4}{3}$