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Show that the following is true. cos(180° - 0) = -cos e

Show that the following is true. cos(180° - 0) = -cos e

Trigonometry (11th Edition)
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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**Verify the Trigonometric Identity** Show that the following is true: \[ \cos(180^\circ - \theta) = -\cos \theta \] ### Explanation This identity can be verified using the properties of the cosine function. - The angle \( 180^\circ - \theta \) is in the second quadrant of the unit circle, where the cosine of an angle is negative. - Using the reference angle, the cosine of \( 180^\circ - \theta \) is the negative of the cosine of \( \theta \). This identity is an example of how trigonometric functions behave under angle transformations, specifically within different quadrants on the unit circle.
Transcribed Image Text:**Verify the Trigonometric Identity** Show that the following is true: \[ \cos(180^\circ - \theta) = -\cos \theta \] ### Explanation This identity can be verified using the properties of the cosine function. - The angle \( 180^\circ - \theta \) is in the second quadrant of the unit circle, where the cosine of an angle is negative. - Using the reference angle, the cosine of \( 180^\circ - \theta \) is the negative of the cosine of \( \theta \). This identity is an example of how trigonometric functions behave under angle transformations, specifically within different quadrants on the unit circle.
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