Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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### Trigonometric Function Exercises #### Problem Statements: (a) **Given:** \( \sin t = 0.31 \) - **Find:** \( \sin(-t) \) - **Answer:** \( \sin(-t) = \) [Input box with X indicating incorrect answer] (b) **Given:** \( \sin \phi = -0.44 \) - **Find:** \( \sin(-\phi) \) - **Answer:** \( \sin(-\phi) = \) [Blank input box] (c) **Given:** \( \cos \alpha = 0.26 \) - **Find:** \( \cos(-\alpha) \) - **Answer:** \( \cos(-\alpha) = \) [Blank input box] (d) **Given:** \( \cos s = -0.59 \) - **Find:** \( \cos(-s) \) - **Answer:** \( \cos(-s) = \) [Blank input box] #### Additional Resources: - **Need Help?** - [Read It] (Button for more information or hints) These exercises aim to practice the properties of sine and cosine functions, specifically focusing on their symmetry properties: - The sine function is odd, meaning \( \sin(-x) = -\sin(x) \). - The cosine function is even, meaning \( \cos(-x) = \cos(x) \). Be sure to use these properties when solving the problems.
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Transcribed Image Text:### Trigonometric Function Exercises #### Problem Statements: (a) **Given:** \( \sin t = 0.31 \) - **Find:** \( \sin(-t) \) - **Answer:** \( \sin(-t) = \) [Input box with X indicating incorrect answer] (b) **Given:** \( \sin \phi = -0.44 \) - **Find:** \( \sin(-\phi) \) - **Answer:** \( \sin(-\phi) = \) [Blank input box] (c) **Given:** \( \cos \alpha = 0.26 \) - **Find:** \( \cos(-\alpha) \) - **Answer:** \( \cos(-\alpha) = \) [Blank input box] (d) **Given:** \( \cos s = -0.59 \) - **Find:** \( \cos(-s) \) - **Answer:** \( \cos(-s) = \) [Blank input box] #### Additional Resources: - **Need Help?** - [Read It] (Button for more information or hints) These exercises aim to practice the properties of sine and cosine functions, specifically focusing on their symmetry properties: - The sine function is odd, meaning \( \sin(-x) = -\sin(x) \). - The cosine function is even, meaning \( \cos(-x) = \cos(x) \). Be sure to use these properties when solving the problems.
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