Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Trigonometry Problem on Cosine Calculation
**Problem 26:**
The terminal ray of an angle extends from the origin out through the point (-11, 4). What is the cosine of that angle?
#### Steps to Solve:
1. **Determine the components:**
- The point given is (-11, 4), where \( x = -11 \) and \( y = 4 \).
2. **Calculate the hypotenuse (r):**
- The hypotenuse \( r \) can be found using the Pythagorean theorem:
\[
r = \sqrt{x^2 + y^2} = \sqrt{(-11)^2 + 4^2} = \sqrt{121 + 16} = \sqrt{137}
\]
3. **Calculate cosine:**
- Cosine of an angle in standard position is calculated as:
\[
\cos(\theta) = \frac{x}{r}
\]
In this scenario, it would be:
\[
\cos(\theta) = \frac{-11}{\sqrt{137}}
\]
- For simplicity, \( \cos(\theta) \approx \frac{-11}{11.7} \approx -0.94 \).
Hence, the cosine of the angle formed by the terminal ray passing through the point (-11, 4) is approximately \( -0.94 \).
---
**Note**: The explanation focuses on ensuring that students can follow the steps and understand how to apply the Pythagorean theorem and the definition of cosine to find the solution. The approximation is provided for simplicity, but students should understand the exact form as well.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba874e82-f331-4b1e-9400-f6613fffe075%2Ff1e57da1-899f-4ded-9aa8-7bf3e9759e11%2Fq8q7h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem on Cosine Calculation
**Problem 26:**
The terminal ray of an angle extends from the origin out through the point (-11, 4). What is the cosine of that angle?
#### Steps to Solve:
1. **Determine the components:**
- The point given is (-11, 4), where \( x = -11 \) and \( y = 4 \).
2. **Calculate the hypotenuse (r):**
- The hypotenuse \( r \) can be found using the Pythagorean theorem:
\[
r = \sqrt{x^2 + y^2} = \sqrt{(-11)^2 + 4^2} = \sqrt{121 + 16} = \sqrt{137}
\]
3. **Calculate cosine:**
- Cosine of an angle in standard position is calculated as:
\[
\cos(\theta) = \frac{x}{r}
\]
In this scenario, it would be:
\[
\cos(\theta) = \frac{-11}{\sqrt{137}}
\]
- For simplicity, \( \cos(\theta) \approx \frac{-11}{11.7} \approx -0.94 \).
Hence, the cosine of the angle formed by the terminal ray passing through the point (-11, 4) is approximately \( -0.94 \).
---
**Note**: The explanation focuses on ensuring that students can follow the steps and understand how to apply the Pythagorean theorem and the definition of cosine to find the solution. The approximation is provided for simplicity, but students should understand the exact form as well.
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