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Home > A2C > Chapter 8 > Lesson 8.1.6 > Problem 8-92


Find the exact values of the angles that are solutions to the equation . Express your solutions in radians. .

Draw a unit circle and a triangle with the opposite side of 0.5 and hypotenuse 1.
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:   8-92 HW eTool