Exercise 6 Page 811

A quadrantal angle is an angle in standard position whose terminal side lies on one of the axes. If θ is a nonquadrantal angle in standard position, its reference angle θ ' is the acute angle formed by the terminal side of θ and the x-axis. Let's recall the rules for finding the measures of reference angles in the four quadrants.

Let's graph the given angle θ =- 3π4. Recall that when an angle has a negative measure, it is being measured clockwise.

If the measure of θ is greater than 2π or less than 0, we use a coterminal angle with a positive measure between 0 and 2π to find the reference angle. To do so, we will add 2π to the given angle.

Let's simplify the addition.

We will add the obtained value to our diagram.

We can see that the terminal side of the angle is located in Quadrant III. Therefore, to find its reference angle θ ' we need to subtract π from 5π4.

Finally, let's simplify the subtraction.

The reference angle is θ '= π4.