Find all solutions for each equation in the interval [0", 360°). 31. 4cos 0-2/3 = 0 32. 2sin 0-sin 0 1
Find all solutions for each equation in the interval [0", 360°). 31. 4cos 0-2/3 = 0 32. 2sin 0-sin 0 1
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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![## Trigonometric Equations
### Instructions:
Find all solutions for each equation in the interval \([0^\circ, 360^\circ]\).
### Equations:
**31.** \[4 \cos \theta - 2\sqrt{3} = 0\]
Solve the equation for \(\theta\), ensuring that \(\theta\) falls within the specified interval.
**32.** \[2 \sin^2 \theta - \sin \theta = 1\]
Similarly, solve this equation within the provided interval.
### Explanation of Symbols:
- \(\theta\): The variable representing the angle in degrees.
- \(\cos\): Cosine function.
- \(\sin\): Sine function.
- \(\sqrt{3}\): Square root of 3.
- \([0^\circ, 360^\circ]\): The interval within which to find the solutions, inclusive of 0 degrees and 360 degrees.
Note: Since this is purely a text-based problem set, no graphs or diagrams are provided. If you require visual aids or further explanation, refer to trigonometric function graphs or unit circle diagrams typically provided in mathematics textbooks or online resources.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0f29cc-98be-45bb-9fb8-5b9efd247a01%2Fb7f4a74a-6443-4f14-963a-9adbd44c8d20%2F98mp798_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Trigonometric Equations
### Instructions:
Find all solutions for each equation in the interval \([0^\circ, 360^\circ]\).
### Equations:
**31.** \[4 \cos \theta - 2\sqrt{3} = 0\]
Solve the equation for \(\theta\), ensuring that \(\theta\) falls within the specified interval.
**32.** \[2 \sin^2 \theta - \sin \theta = 1\]
Similarly, solve this equation within the provided interval.
### Explanation of Symbols:
- \(\theta\): The variable representing the angle in degrees.
- \(\cos\): Cosine function.
- \(\sin\): Sine function.
- \(\sqrt{3}\): Square root of 3.
- \([0^\circ, 360^\circ]\): The interval within which to find the solutions, inclusive of 0 degrees and 360 degrees.
Note: Since this is purely a text-based problem set, no graphs or diagrams are provided. If you require visual aids or further explanation, refer to trigonometric function graphs or unit circle diagrams typically provided in mathematics textbooks or online resources.
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