0 12 cos 90°
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 Values at Specific Angles**
In trigonometry, certain angles often have well-known values for functions like the cosine (\( \cos \)) and tangent (\( \tan \)) functions. Below are examples of such calculations:
1. **Cosine of 90 Degrees:**
\[ \cos 90^\circ \]
2. **Tangent of 135 Degrees:**
\[ \tan 135^\circ \]
**Explanation:**
### Cosine Function
- The cosine of 90 degrees (\( \cos 90^\circ \)) is 0. In the unit circle, the value is derived from the \( x \)-coordinate and at 90 degrees (or \( \frac{\pi}{2} \) radians), the \( x \)-coordinate is 0.
### Tangent Function
- The tangent of 135 degrees (\( \tan 135^\circ \)) can be calculated as the tangent of 180 degrees minus 45 degrees.
\[ \tan 135^\circ = \tan (180^\circ - 45^\circ) = -\tan 45^\circ = -1 \]
Understanding the values at these specific angles is fundamental in trigonometry, helping to solve more complex problems in mathematics, physics, and engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee38ad10-d3a7-46a8-a0c4-2e1f024f265a%2F42d3198f-1689-4e25-a5e9-0e243e0f3e1f%2F8rqxnn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Trigonometric Values at Specific Angles**
In trigonometry, certain angles often have well-known values for functions like the cosine (\( \cos \)) and tangent (\( \tan \)) functions. Below are examples of such calculations:
1. **Cosine of 90 Degrees:**
\[ \cos 90^\circ \]
2. **Tangent of 135 Degrees:**
\[ \tan 135^\circ \]
**Explanation:**
### Cosine Function
- The cosine of 90 degrees (\( \cos 90^\circ \)) is 0. In the unit circle, the value is derived from the \( x \)-coordinate and at 90 degrees (or \( \frac{\pi}{2} \) radians), the \( x \)-coordinate is 0.
### Tangent Function
- The tangent of 135 degrees (\( \tan 135^\circ \)) can be calculated as the tangent of 180 degrees minus 45 degrees.
\[ \tan 135^\circ = \tan (180^\circ - 45^\circ) = -\tan 45^\circ = -1 \]
Understanding the values at these specific angles is fundamental in trigonometry, helping to solve more complex problems in mathematics, physics, and engineering.
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