Chapter 4, Problem 6CT

To determine

To find: the reference angle ${\theta }^{\prime }$ of the angle $\theta =205°$ and sketch $\theta$ in standard position and label ${\theta }^{\prime }$ .

Answer to Problem 6CT

  ${\theta }^{\prime }=25°$

  

Explanation of Solution

Concept used:

Reference angle ${\theta }^{\prime }$ depends on the quadrant in which the angle $\theta$ lies.

If $\theta$ lies in 2^nd quadrant, reference angle is ${\theta }^{\prime }=180°-\theta$ .

If $\theta$ lies in 3^rd quadrant, reference angle is ${\theta }^{\prime }=\theta -180°$ .

If $\theta$ lies in 4^th quadrant, reference angle is ${\theta }^{\prime }=360°-\theta$ .

Since, the angle $\theta =205°$ lies in 3^rd quadrant, so the reference angle is:

  $\begin{array}{c}{\theta }^{\prime }=\theta -180°\\ =205°-180°\\ =25°\end{array}$

The sketch of the angle $\theta =205°$ in standard position is given below: