Answered: Determine a coterminal angle of 690°.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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$**Determining a Coterminal Angle of 690°** Coterminal angles are angles that share the same initial and terminal sides, but may have different measures. You can find coterminal angles by adding or subtracting full rotations (360°) from the given angle. To find a coterminal angle of 690°: 1. Subtract 360° from 690° until you obtain an angle between 0° and 360°. \[ 690° - 360° = 330° \] Thus, 330° is a coterminal angle of 690°. **Explanation with Diagram:** Imagine the coordinate plane with the standard position of angles. The initial side of the angle is along the positive x-axis. Each full rotation (360°) brings you back to the starting point. - Start at 0° along the positive x-axis. - Rotate counterclockwise by 690° (this includes one full rotation of 360° plus an additional 330°). On subtracting 360° from 690°: - The first subtraction gives 330°, which is within the range from 0° to 360°. Therefore, the angle 330° is coterminal with the given angle of 690°. A simple way to visualize this is by drawing a circle and marking the angles. Consequently, both 690° and 330° will have their terminal side coinciding. This method can easily be used to find coterminal angles for any given angle.$

Transcribed Image Text:**Determining a Coterminal Angle of 690°** Coterminal angles are angles that share the same initial and terminal sides, but may have different measures. You can find coterminal angles by adding or subtracting full rotations (360°) from the given angle. To find a coterminal angle of 690°: 1. Subtract 360° from 690° until you obtain an angle between 0° and 360°. \[ 690° - 360° = 330° \] Thus, 330° is a coterminal angle of 690°. **Explanation with Diagram:** Imagine the coordinate plane with the standard position of angles. The initial side of the angle is along the positive x-axis. Each full rotation (360°) brings you back to the starting point. - Start at 0° along the positive x-axis. - Rotate counterclockwise by 690° (this includes one full rotation of 360° plus an additional 330°). On subtracting 360° from 690°: - The first subtraction gives 330°, which is within the range from 0° to 360°. Therefore, the angle 330° is coterminal with the given angle of 690°. A simple way to visualize this is by drawing a circle and marking the angles. Consequently, both 690° and 330° will have their terminal side coinciding. This method can easily be used to find coterminal angles for any given angle.