Express the following as a function of a positive acute angle: cos 242°
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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![### Problem:
**Express the following as a function of a positive acute angle:**
\[ \cos 242^\circ \]
### Explanation:
To convert \(\cos 242^\circ \) into the function of a positive acute angle:
1. **Understand the angle location**:
- \(242^\circ\) is in the third quadrant since it is between \(180^\circ\) and \(270^\circ\).
2. **Reference angle calculation**:
- The reference angle for an angle in the third quadrant is determined by subtracting \(180^\circ\) from the given angle:
\[
242^\circ - 180^\circ = 62^\circ
\]
3. **Cosine function properties**:
- The cosine of an angle in the third quadrant is negative.
- Therefore, \(\cos 242^\circ\) is equal to the negative of the cosine of its reference angle \(62^\circ\).
4. **Expressing the function**:
\[
\cos 242^\circ = -\cos 62^\circ
\]
So, the final expression is:
\[ \cos 242^\circ = -\cos 62^\circ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8768ead9-4386-4320-b58b-e10301956e77%2Fbd423d29-c02a-4d40-9ed5-0beb2f1cb92d%2Fuvc2xhl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem:
**Express the following as a function of a positive acute angle:**
\[ \cos 242^\circ \]
### Explanation:
To convert \(\cos 242^\circ \) into the function of a positive acute angle:
1. **Understand the angle location**:
- \(242^\circ\) is in the third quadrant since it is between \(180^\circ\) and \(270^\circ\).
2. **Reference angle calculation**:
- The reference angle for an angle in the third quadrant is determined by subtracting \(180^\circ\) from the given angle:
\[
242^\circ - 180^\circ = 62^\circ
\]
3. **Cosine function properties**:
- The cosine of an angle in the third quadrant is negative.
- Therefore, \(\cos 242^\circ\) is equal to the negative of the cosine of its reference angle \(62^\circ\).
4. **Expressing the function**:
\[
\cos 242^\circ = -\cos 62^\circ
\]
So, the final expression is:
\[ \cos 242^\circ = -\cos 62^\circ \]
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