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The expression sin(r) cos(40°) – cos(x) sin(40°) equals i) sin(x – 40°) ii) cos(r – 40°) iii) sin(x + 40°) iv) not listed

The expression sin(r) cos(40°) – cos(x) sin(40°) equals i) sin(x – 40°) ii) cos(r – 40°) iii) sin(x + 40°) iv) not listed

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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The problem presented is as follows: 11. The expression \( \sin(x) \cos(40^\circ) - \cos(x) \sin(40^\circ) \) equals i) \( \sin(x - 40^\circ) \)   ii) \( \cos(x - 40^\circ) \)   iii) \( \sin(x + 40^\circ) \)   iv) not listed This is a trigonometric identity problem aiming to determine which option matches the expression given. The expression \( \sin(x) \cos(40^\circ) - \cos(x) \sin(40^\circ) \) uses the sine subtraction formula, which states that \( \sin(A - B) = \sin A \cos B - \cos A \sin B \).
Transcribed Image Text:The problem presented is as follows: 11. The expression \( \sin(x) \cos(40^\circ) - \cos(x) \sin(40^\circ) \) equals i) \( \sin(x - 40^\circ) \)   ii) \( \cos(x - 40^\circ) \)   iii) \( \sin(x + 40^\circ) \)   iv) not listed This is a trigonometric identity problem aiming to determine which option matches the expression given. The expression \( \sin(x) \cos(40^\circ) - \cos(x) \sin(40^\circ) \) uses the sine subtraction formula, which states that \( \sin(A - B) = \sin A \cos B - \cos A \sin B \).
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