Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter3: Multi-step Equations And Inequalities
Section: Chapter Questions
Problem 11PTTS
Related questions
Question
![**Problem Statement:**
Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 315°.
\( (x, y) = ( \_\_\_\_\_ \_\_\_\_\_, \_\_\_\_\_ \_\_\_\_\_ ) \)
**Instruction:**
Round your answers to three decimal places.
**Explanation:**
This is a trigonometric problem where you need to find the coordinates \((x, y)\) of a point on a circle with a given radius and angle. The formula to find the coordinates \((x, y)\) of a point on a circle with radius \(r\) and angle \(\theta\) (in degrees) is:
\[ x = r \cdot \cos(\theta) \]
\[ y = r \cdot \sin(\theta) \]
Given:
- Radius \(r\) = 20
- Angle \(\theta\) = 315°
Convert the angle to radians if necessary and then substitute the values into the formulas to find \(x\) and \(y\). Finally, round the answers to three decimal places as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d8b0e94-47ef-477e-9622-abc8b98247d8%2F01e8c198-61ec-4651-8576-6b09b05e59c7%2Fmuizxve_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 315°.
\( (x, y) = ( \_\_\_\_\_ \_\_\_\_\_, \_\_\_\_\_ \_\_\_\_\_ ) \)
**Instruction:**
Round your answers to three decimal places.
**Explanation:**
This is a trigonometric problem where you need to find the coordinates \((x, y)\) of a point on a circle with a given radius and angle. The formula to find the coordinates \((x, y)\) of a point on a circle with radius \(r\) and angle \(\theta\) (in degrees) is:
\[ x = r \cdot \cos(\theta) \]
\[ y = r \cdot \sin(\theta) \]
Given:
- Radius \(r\) = 20
- Angle \(\theta\) = 315°
Convert the angle to radians if necessary and then substitute the values into the formulas to find \(x\) and \(y\). Finally, round the answers to three decimal places as instructed.
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