Given the cartesian point (-5, -11) find the polar point (r, 0) where is measured in degrees
Given the cartesian point (-5, -11) find the polar point (r, 0) where is measured in degrees
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
![**Converting Cartesian to Polar Coordinates: A Step-by-Step Guide**
**Problem Statement:**
Given the Cartesian point \((-5, -11)\), find the polar point \((r, \theta)\) where \(\theta\) is measured in degrees.
**Explanation:**
To convert Cartesian coordinates \((x, y)\) to polar coordinates \((r, \theta)\), use the following formulas:
1. **\(r\) Calculation:**
\[
r = \sqrt{x^2 + y^2}
\]
Here, \(x = -5\) and \(y = -11\).
2. **\(\theta\) Calculation:**
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Ensure \(\theta\) is in the correct quadrant. Since both \(x\) and \(y\) are negative, \(\theta\) will be in the third quadrant.
Converting the polar angle from radians to degrees if needed.
**Illustrative Diagrams:**
- **Cartesian Plane:** Diagram showing the point \((-5, -11)\).
- **Polar Plane:** Diagram showing the equivalent polar coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb77dd63d-90e0-4a84-b222-b885a237b41a%2Fb0bdb9ec-2cd0-40d5-81a7-6869c2dee1a5%2Frotveh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Converting Cartesian to Polar Coordinates: A Step-by-Step Guide**
**Problem Statement:**
Given the Cartesian point \((-5, -11)\), find the polar point \((r, \theta)\) where \(\theta\) is measured in degrees.
**Explanation:**
To convert Cartesian coordinates \((x, y)\) to polar coordinates \((r, \theta)\), use the following formulas:
1. **\(r\) Calculation:**
\[
r = \sqrt{x^2 + y^2}
\]
Here, \(x = -5\) and \(y = -11\).
2. **\(\theta\) Calculation:**
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Ensure \(\theta\) is in the correct quadrant. Since both \(x\) and \(y\) are negative, \(\theta\) will be in the third quadrant.
Converting the polar angle from radians to degrees if needed.
**Illustrative Diagrams:**
- **Cartesian Plane:** Diagram showing the point \((-5, -11)\).
- **Polar Plane:** Diagram showing the equivalent polar coordinates.
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