# Given cotphi=-3, sinphi=sqrt10/10 to find the remaining trigonometric function?

Mar 5, 2017

See explanation.

#### Explanation:

Using the equality:

## $\tan \phi \cdot \cot \phi = 1$

we get that: $\cot \phi = - \frac{1}{3}$

To calculate $\cos \phi$ we can use the equality:

## $\cot \phi = \cos \frac{\phi}{\sin} \phi$

$\cos \frac{\phi}{\frac{\sqrt{10}}{10}} = - 3$

From this we know that:

$\cos \phi = \frac{- 3 \sqrt{10}}{10}$

Finally we can write the 4 values:

$\left\{\begin{matrix}\sin \phi = \frac{\sqrt{10}}{10} \\ \cos \phi = \frac{- 3 \sqrt{10}}{10} \\ \tan \phi = - 3 \\ \cot \phi = - \frac{1}{3}\end{matrix}\right.$