Chapter 12.3, Problem 9OE

To determine

For angle $\theta$ , find its quadrant and its refrence angle.

Answer to Problem 9OE

  $\theta =-305°$ is in Quadrant I and its reference angle is $\alpha =55°$

Explanation of Solution

Given:

  $\theta =-305°$

Formula Used:

If $\theta$ is not a quadrantal angle, there is a unique acute angle $\alpha$ corresponding to $\theta$ , formed by the terminal side of $\theta$ and the positive or negative x- axis.When $\theta$ is in standard position , $\alpha$ is called the reference angle of $\theta$ .

Calculation:

Since the angle is negative, first add it to $360°$ to get the anti-clockwise angle

  $360°-305°=55°$

  $0°<\theta \text{'}=55°<90°$ , the angle is in quadrant I.So, the reference angle is :

  $\alpha =55°$