### Home > INT3 > Chapter 9 > Lesson 9.1.6 > Problem 9-78

Calculate the exact values of the angles that are solutions to the equation sin(*θ*) = 0.5. Express your solutions in radians. *9-78 HW eTool* (Desmos). Homework Help ✎

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 30°-60°-90° triangle. *θ* = 30°.

Reflect the triangle across the *y*-axis. If 30° is the reference angle, what is the circular angle?

Notice that *θ* = 150° as well.

Convert both angles to radians. Recall that 180° is *π* radians. What fraction of 180° is 150°?

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 360° or 2*π* 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*.