Express cos K as a fraction in simplest 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°.
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Question
![### Identifying Trigonometric Ratios
**Example Problem:**
**User: Kiera Osborne**
**Topic: Identifying Trig Ratios (Diagram), Level 1**
**Date: Jun 01, 12:09:51 PM**
#### Problem Statement
**Express cos \( K \) as a fraction in simplest terms.**
#### Diagram Description
In the diagram, we have a right triangle with the following specifications:
- The hypotenuse is labeled with the length of 23.
- One leg adjacent to angle \( K \) has a length of 5.
- The other leg, opposite angle \( K \), is not labeled with a length.
\[ \triangle \text{Triangle: Right Angle, Labelled distances}\]
To solve for cos \( K \), recall the definition of cosine in a right triangle:
\[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
With the lengths provided:
- Adjacent side to angle \( K \) = 5
- Hypotenuse = 23
Therefore,
\[ \cos(K) = \frac{5}{23} \]
**Answer:**
\[ \cos K = \frac{5}{23} \]
#### Solution Box
\[ \text{Answer: cos \( K \) = } \underline{\: \: \: \: \: \_ \: \: \: \: \: \_ \: \: \: \: \: } \]
**Submit the Answer** button located on the interface to validate the response.
**Note:**
Given that the user has an ongoing record and score, always double-check values and terms provided in problems for accuracy before submitting. Adjust fractions or terms if necessary to ensure they are in the simplest form.
---
**Educational Value:**
Understanding the fundamentals of trigonometric ratios in right triangles is crucial for trigonometry. Being able to identify and compute these ratios forms the basis for more complex applications in geometry, algebra, calculus, and real-world problem solving.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19a52d56-c74a-446f-8187-bbcc4eedbfac%2F2ae21617-a6a7-484c-8d1e-3371c177adb4%2F7ee82qr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Identifying Trigonometric Ratios
**Example Problem:**
**User: Kiera Osborne**
**Topic: Identifying Trig Ratios (Diagram), Level 1**
**Date: Jun 01, 12:09:51 PM**
#### Problem Statement
**Express cos \( K \) as a fraction in simplest terms.**
#### Diagram Description
In the diagram, we have a right triangle with the following specifications:
- The hypotenuse is labeled with the length of 23.
- One leg adjacent to angle \( K \) has a length of 5.
- The other leg, opposite angle \( K \), is not labeled with a length.
\[ \triangle \text{Triangle: Right Angle, Labelled distances}\]
To solve for cos \( K \), recall the definition of cosine in a right triangle:
\[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
With the lengths provided:
- Adjacent side to angle \( K \) = 5
- Hypotenuse = 23
Therefore,
\[ \cos(K) = \frac{5}{23} \]
**Answer:**
\[ \cos K = \frac{5}{23} \]
#### Solution Box
\[ \text{Answer: cos \( K \) = } \underline{\: \: \: \: \: \_ \: \: \: \: \: \_ \: \: \: \: \: } \]
**Submit the Answer** button located on the interface to validate the response.
**Note:**
Given that the user has an ongoing record and score, always double-check values and terms provided in problems for accuracy before submitting. Adjust fractions or terms if necessary to ensure they are in the simplest form.
---
**Educational Value:**
Understanding the fundamentals of trigonometric ratios in right triangles is crucial for trigonometry. Being able to identify and compute these ratios forms the basis for more complex applications in geometry, algebra, calculus, and real-world problem solving.
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