Find each of the following for y in radians. 28. y arcsin
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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Question
![### Finding Angles for Inverse Trigonometric Functions
Find each of the following for \( y \) in radians.
**Problem 28:**
\[ y = \arcsin \left( \frac{\sqrt{3}}{2} \right) \]
**Problem 29:**
\[ y = \cos^{-1} \left( -\frac{1}{2} \right) \]
**Problem 30:**
\[ y = \arctan(-1) \]
### Explanation:
These problems involve finding the angle \( y \) in radians that satisfies the given inverse trigonometric function:
1. **Problem 28**: We need to find the angle \( y \) such that \( \sin(y) = \frac{\sqrt{3}}{2} \). This corresponds to an angle in the first or second quadrant where the sine value is \( \frac{\sqrt{3}}{2} \).
2. **Problem 29**: Here, we seek the angle \( y \) such that \( \cos(y) = -\frac{1}{2} \). This corresponds to an angle in the second or third quadrant where the cosine value is \( -\frac{1}{2} \).
3. **Problem 30**: We need to identify the angle \( y \) such that \( \tan(y) = -1 \). This corresponds to an angle in the second or fourth quadrant where the tangent value is \( -1 \).
These problems are important for understanding how to work with inverse trigonometric functions and converting values of sine, cosine, and tangent back into angle measures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0f29cc-98be-45bb-9fb8-5b9efd247a01%2F021d5cdc-56e3-44cf-a3d0-0832973f4e36%2Fnl75cns_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding Angles for Inverse Trigonometric Functions
Find each of the following for \( y \) in radians.
**Problem 28:**
\[ y = \arcsin \left( \frac{\sqrt{3}}{2} \right) \]
**Problem 29:**
\[ y = \cos^{-1} \left( -\frac{1}{2} \right) \]
**Problem 30:**
\[ y = \arctan(-1) \]
### Explanation:
These problems involve finding the angle \( y \) in radians that satisfies the given inverse trigonometric function:
1. **Problem 28**: We need to find the angle \( y \) such that \( \sin(y) = \frac{\sqrt{3}}{2} \). This corresponds to an angle in the first or second quadrant where the sine value is \( \frac{\sqrt{3}}{2} \).
2. **Problem 29**: Here, we seek the angle \( y \) such that \( \cos(y) = -\frac{1}{2} \). This corresponds to an angle in the second or third quadrant where the cosine value is \( -\frac{1}{2} \).
3. **Problem 30**: We need to identify the angle \( y \) such that \( \tan(y) = -1 \). This corresponds to an angle in the second or fourth quadrant where the tangent value is \( -1 \).
These problems are important for understanding how to work with inverse trigonometric functions and converting values of sine, cosine, and tangent back into angle measures.
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