Exercise 55 Page 828

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 = 54π.

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 54π.

The reference angle is θ ' = π4.