CPM Homework Help : A2C Problem 13-30

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13-30.

Jeremy used the $\operatorname{sin}^{−1}$ button on his calculator to solve a trigonometric equation and got the solution $37°$ . He knows that there must be more than one solution. What are the rest of the solutions to Jeremy's equation? Explain how you found them. Use a unit circle and a graph in your explanation.

Using a unit circle:

Step 1 (unit circle):

Draw a Unit circle and estimate 37 degrees.

Step 2 (unit circle):

Since sin is height, draw in the height to the x-axis.

Step 3 (unit circle):

Find and draw the same height any other place it may occur on the unit circle.

Step 4 (unit circle):

Calculate the new angles.

Answer (unit circle):

$180° − 37° = 143°$ , so $37 + 2πn$ and $143 + 2πn$ where n is any integer.