cos 300⁰
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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![**Topic: Evaluating Trigonometric Functions**
For this section, we will calculate the cosine of 300 degrees.
**cos 300°**
To evaluate the cosine of 300 degrees, we can use the unit circle or trigonometric identities.
1. **Using the Unit Circle:**
- The angle 300° is located in the fourth quadrant of the unit circle.
- The reference angle for 300° is 360° - 300° = 60°.
- In the fourth quadrant, the cosine function is positive since it corresponds to the x-coordinate of the unit circle at that angle.
Therefore:
\[ \cos 300° = \cos 60° \]
2. **Evaluating cos 60°:**
- From trigonometric tables or the unit circle, we know that:
\[ \cos 60° = \frac{1}{2} \]
Hence:
\[ \cos 300° = \frac{1}{2} \]
**Conclusion:**
The value of cos 300° is 0.5.
---
**Interactive Element:**
- Practice calculating the cosine values of other angles using the unit circle method.
- Explore other trigonometric functions like sine and tangent for various angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee38ad10-d3a7-46a8-a0c4-2e1f024f265a%2F45f2d6aa-4cf3-4c12-9fea-d038331fdd00%2F3kflzv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Evaluating Trigonometric Functions**
For this section, we will calculate the cosine of 300 degrees.
**cos 300°**
To evaluate the cosine of 300 degrees, we can use the unit circle or trigonometric identities.
1. **Using the Unit Circle:**
- The angle 300° is located in the fourth quadrant of the unit circle.
- The reference angle for 300° is 360° - 300° = 60°.
- In the fourth quadrant, the cosine function is positive since it corresponds to the x-coordinate of the unit circle at that angle.
Therefore:
\[ \cos 300° = \cos 60° \]
2. **Evaluating cos 60°:**
- From trigonometric tables or the unit circle, we know that:
\[ \cos 60° = \frac{1}{2} \]
Hence:
\[ \cos 300° = \frac{1}{2} \]
**Conclusion:**
The value of cos 300° is 0.5.
---
**Interactive Element:**
- Practice calculating the cosine values of other angles using the unit circle method.
- Explore other trigonometric functions like sine and tangent for various angles.
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