ALL E Sin 2COS
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°.
Related questions
Question
![The image contains the mathematical expression:
\[ 3 \sin (\cos^{-1}(-\frac{1}{2})) \]
This expression involves trigonometric functions, specifically the sine and the inverse cosine (arccos) functions.
Explanation:
- \(\cos^{-1}(-\frac{1}{2})\) is the inverse cosine function, which finds the angle whose cosine value is \(-\frac{1}{2}\).
- The sine function \(\sin\) is then applied to this angle.
- The result is multiplied by 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60a45696-62af-4159-8f12-2afd2f9f3f3b%2Faafe6fc9-4e21-4280-aa47-5a8cf659a3eb%2Fz3tgqh_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains the mathematical expression:
\[ 3 \sin (\cos^{-1}(-\frac{1}{2})) \]
This expression involves trigonometric functions, specifically the sine and the inverse cosine (arccos) functions.
Explanation:
- \(\cos^{-1}(-\frac{1}{2})\) is the inverse cosine function, which finds the angle whose cosine value is \(-\frac{1}{2}\).
- The sine function \(\sin\) is then applied to this angle.
- The result is multiplied by 3.
![### Trigonometric Equations and Solutions
This section will explore how to find all solutions for specific trigonometric equations.
#### Given Equations
1. **Equation 1:**
\[
\sin(\theta) = -\frac{\sqrt{3}}{2}
\]
2. **Equation 2:**
\[
2\cos(2\theta) = -1
\]
#### Objective
- Find **all 8 solutions** for the above trigonometric equations.
These problems involve using fundamental trigonometric identities and properties to solve for the angle \(\theta\). The solutions to such equations are found by identifying specific reference angles and their corresponding positions on the unit circle, as well as using double angle identities for cosine.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60a45696-62af-4159-8f12-2afd2f9f3f3b%2Faafe6fc9-4e21-4280-aa47-5a8cf659a3eb%2Fl7jnl5h_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometric Equations and Solutions
This section will explore how to find all solutions for specific trigonometric equations.
#### Given Equations
1. **Equation 1:**
\[
\sin(\theta) = -\frac{\sqrt{3}}{2}
\]
2. **Equation 2:**
\[
2\cos(2\theta) = -1
\]
#### Objective
- Find **all 8 solutions** for the above trigonometric equations.
These problems involve using fundamental trigonometric identities and properties to solve for the angle \(\theta\). The solutions to such equations are found by identifying specific reference angles and their corresponding positions on the unit circle, as well as using double angle identities for cosine.
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