Q 92. - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(\theta \right)=cot \theta =-2$ find $f\left(\theta +\pi \right)$.

Step-by-Step Solution

Answer

The value of $f\left(\theta +\pi \right)$ is $\frac{1}{2}$.

Step 1. Given information.

Consider the given information $f\left(\theta \right)=cot \theta$ and the value of $cot \theta =-2$.

Step 2. Formula used.

$cot \left(A+B\right)=\frac{cot A cot B-1}{cot A+cot B}$

Step 3. Finding the value of f θ + π .

Substitute the value in formula.

$$\begin{gathered} cot \left(A+B\right)=\frac{cot Acot B-1}{cot A+cot B} \\ cot\left(A+B\right)=\frac{1}{2} \end{gathered}$$

Therefore the value of $f\left(\theta +\pi \right)$ is $\frac{1}{2}$.