Homework Help is Here – Start Your Trial Now!
Math
Trigonometry
r = 1+2 cos 0 r Check for symmetry polar axis line 0 = " 2 pole 一3

r = 1+2 cos 0 r Check for symmetry polar axis line 0 = " 2 pole 一3

Trigonometry (11th Edition)
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°.
See similar textbooks
Question

Test for symmetry and graph each polar equation for r=1+2cosθ.

### Polar Equation Analysis #### Given Equation: \[ r = 1 + 2 \cos \theta \] #### Table of Values | \( \theta \) | 0 | \( \frac{\pi}{6} \) | \( \frac{\pi}{3} \) | \( \frac{\pi}{2} \) | \( \frac{2\pi}{3} \) | \( \frac{5\pi}{6} \) | \( \pi \) | |--------------|---|------------------|------------------|------------------|------------------|------------------|---| | \( r \) | | | | | | | | #### Symmetry Check - **Polar Axis:** - **Line \( \theta = \frac{\pi}{2} \):** - **Pole:** #### Graph Description: The diagram is a polar coordinate graph with circular grids and radial lines, centered at the pole (origin). It consists of concentric circles increasing in radius and radial lines dividing the plane into equal angular sections. Each axis is marked, allowing for plotting polar equations by calculating \( r \) for different angles \( \theta \). This analysis involves calculating values of \( r \) for given angles and checking symmetrical properties of the polar graph defined by the equation \( r = 1 + 2 \cos \theta \).
Transcribed Image Text:### Polar Equation Analysis #### Given Equation: \[ r = 1 + 2 \cos \theta \] #### Table of Values | \( \theta \) | 0 | \( \frac{\pi}{6} \) | \( \frac{\pi}{3} \) | \( \frac{\pi}{2} \) | \( \frac{2\pi}{3} \) | \( \frac{5\pi}{6} \) | \( \pi \) | |--------------|---|------------------|------------------|------------------|------------------|------------------|---| | \( r \) | | | | | | | | #### Symmetry Check - **Polar Axis:** - **Line \( \theta = \frac{\pi}{2} \):** - **Pole:** #### Graph Description: The diagram is a polar coordinate graph with circular grids and radial lines, centered at the pole (origin). It consists of concentric circles increasing in radius and radial lines dividing the plane into equal angular sections. Each axis is marked, allowing for plotting polar equations by calculating \( r \) for different angles \( \theta \). This analysis involves calculating values of \( r \) for given angles and checking symmetrical properties of the polar graph defined by the equation \( r = 1 + 2 \cos \theta \).
This image depicts a polar coordinate grid, commonly used in mathematics and engineering to represent data in a circular layout. The grid features: 1. **Concentric Circles:** These circles radiate outward from the center, serving as guides for measuring distances from the origin. Each circle is labeled with even numbers (0, 2, 4, 6, 8, 10), indicating the radial distance. 2. **Radial Lines:** These lines emanate from the center of the grid, dividing the circle into equal angular sections. The lines intersect each circle at equal intervals. 3. **Axes:** The horizontal and vertical lines are the principal axes of this grid, marked with arrows indicating positive directions. Each axis is labeled with numbers (-10, -5, 0, 5, 10), denoting points along the axes. This polar grid is often utilized to plot points and curves by using angles and radii, offering an intuitive way to visualize functions and data patterns that have rotational symmetry or cyclical trends.
Transcribed Image Text:This image depicts a polar coordinate grid, commonly used in mathematics and engineering to represent data in a circular layout. The grid features: 1. **Concentric Circles:** These circles radiate outward from the center, serving as guides for measuring distances from the origin. Each circle is labeled with even numbers (0, 2, 4, 6, 8, 10), indicating the radial distance. 2. **Radial Lines:** These lines emanate from the center of the grid, dividing the circle into equal angular sections. The lines intersect each circle at equal intervals. 3. **Axes:** The horizontal and vertical lines are the principal axes of this grid, marked with arrows indicating positive directions. Each axis is labeled with numbers (-10, -5, 0, 5, 10), denoting points along the axes. This polar grid is often utilized to plot points and curves by using angles and radii, offering an intuitive way to visualize functions and data patterns that have rotational symmetry or cyclical trends.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Polar Equations of Conics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS