Find cos o. (8, 6) ? COS O ニ Give your answer in lowest terms.
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°.
Related questions
Question
![**Instructions:**
Find \(\cos \phi\).
**Diagram Description:**
The diagram shows a coordinate plane with a vector \( \mathbf{r} \) originating from the origin (0,0) and pointing to the coordinate (8, 6). The angle \(\phi\) is formed between the positive x-axis and the vector \( \mathbf{r} \).
**Calculation:**
\[
\cos \phi = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
Given the coordinates (8, 6):
- The adjacent side of the angle \(\phi\) is 8 (along the x-axis).
- To find the hypotenuse \( r \), use the formula:
\[
r = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10
\]
Therefore,
\[
\cos \phi = \frac{8}{10}
\]
**Simplified Answer:**
Give your answer in lowest terms:
\[
\cos \phi = \frac{4}{5}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2c9438-5a89-4288-b691-8fe1dc913be9%2Fb2cbd3c1-ff47-47e0-966d-6d76f03a51fe%2Fz96o3ij_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Find \(\cos \phi\).
**Diagram Description:**
The diagram shows a coordinate plane with a vector \( \mathbf{r} \) originating from the origin (0,0) and pointing to the coordinate (8, 6). The angle \(\phi\) is formed between the positive x-axis and the vector \( \mathbf{r} \).
**Calculation:**
\[
\cos \phi = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
Given the coordinates (8, 6):
- The adjacent side of the angle \(\phi\) is 8 (along the x-axis).
- To find the hypotenuse \( r \), use the formula:
\[
r = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10
\]
Therefore,
\[
\cos \phi = \frac{8}{10}
\]
**Simplified Answer:**
Give your answer in lowest terms:
\[
\cos \phi = \frac{4}{5}
\]
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