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Home > A2C > Chapter 13 > Lesson 13.1.2 > Problem 13-30

13-30.

Jeremy used the 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. Homework Help ✎

Using a unit circle:

Draw a Unit circle and estimate 37 degrees.

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

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

Calculate the new angles.

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

Using a graph:

Draw the sine curve.

Draw y = sin(37)

Find the x-values where the two graphs intersect.

Label the solution 37°.

Use Symmetry to find other solutions.