Chapter 12.3, Problem 5OE

To determine

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

Answer to Problem 5OE

  $\theta =170°$ is in 2^nd quadrant and its reference angle is $\alpha =10°$

Explanation of Solution

Given:

  $\theta =170°$

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 $90°<\theta =170°<180°$ , the angle is in 2^nd quadrant.So, the reference angle is :

  $\alpha =180°-\theta =180°-170°=10°$