CPM Homework Banner
9-78.

Calculate the exact values of the angles that are solutions to the equation . Express your solutions in radians. 9-78 HW eTool (Desmos)  Homework Help ✎

Draw a unit circle and a triangle with the opposite side of and hypotenuse .
Since the short leg is half the hypotenuse, this is a triangle. .

Reflect the triangle across the -axis. If is the reference angle, what is the circular angle?
Notice that as well.

Convert both angles to radians. Recall that is radians. What fraction of is ?

Every time you go around the circle, you will come back to these points, so there are an infinite number of solutions to this equation.
A new solution occurs every or  radians.

Use the eTool below to view the solution as a graph.
Click the link at right for the full version of the eTool: INT3 9-78 HW eTool.