Chapter 4, Problem 51RE

To determine

To find: the reference angle ${\theta }^{\prime }$

And sketch $\theta$ and ${\theta }^{\prime }$ in standard position

Answer to Problem 51RE

  $\begin{array}{l}\theta ={264}^0\\ {\theta }^{\prime }={264}^0-{180}^0\\ ={96}^0\end{array}$

Explanation of Solution

Given information:

Angle $\theta ={264}^0$

Formula used:

Reference angle ${\theta }^{\prime }$

If $\theta$ is between ${180}^0-{270}^0$

Then ${\theta }^{\prime }$ is = $\theta -{180}^0$

Calculation:

Consider the statement “find the reference angle ${\theta }^{\prime }$ and sketch it”.

Recall that reference angle ${\theta }^{\prime }$ is

  $\begin{array}{l}=\theta -{180}^0\\ =264-{180}^0\\ ={84}^0\end{array}$

Recall that the standard position is between ${180}^0$ to ${270}^0$

Therefore $\theta ={264}^0$

So, the reference angle ${\theta }^{\prime }$ is ${96}^0$