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Graph and make a table a) r = 2cos 50 b) r=2 sine c) r=1-cost

Graph and make a table a) r = 2cos 50 b) r=2 sine c) r=1-cost

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Graph and Make a Table** This exercise involves graphing polar equations and creating a corresponding table of values for each equation. **Equations:** a) \( r = 2 \cos(5\theta) \) b) \( r = 2 \sin(\theta) \) c) \( r = 1 - \cos(\theta) \) **Instructions:** For each equation above, plot the graph on the respective coordinate system provided. The cross-shaped diagrams represent the polar coordinate systems where you will need to sketch the polar plots for each of the given equations. **Polar Graph Explanation:** 1. **Equation a: \( r = 2 \cos(5\theta) \)** - This is a type of polar graph known as a rose curve. The coefficient 5 in front of \(\theta\) indicates that the graph will have 5 petals. 2. **Equation b: \( r = 2 \sin(\theta) \)** - This is a circle in the polar coordinate system centered on the vertical axis passing through the pole. It has a radius of 1 unit. 3. **Equation c: \( r = 1 - \cos(\theta) \)** - This describes a cardioid, a heart-shaped curve that passes through the pole. When plotting these graphs, consider the domains and follow the curves as \(\theta\) varies from \(0\) to \(2\pi\). Make sure to label important points and axes to aid in the understanding of these polar graphs.
Transcribed Image Text:**Graph and Make a Table** This exercise involves graphing polar equations and creating a corresponding table of values for each equation. **Equations:** a) \( r = 2 \cos(5\theta) \) b) \( r = 2 \sin(\theta) \) c) \( r = 1 - \cos(\theta) \) **Instructions:** For each equation above, plot the graph on the respective coordinate system provided. The cross-shaped diagrams represent the polar coordinate systems where you will need to sketch the polar plots for each of the given equations. **Polar Graph Explanation:** 1. **Equation a: \( r = 2 \cos(5\theta) \)** - This is a type of polar graph known as a rose curve. The coefficient 5 in front of \(\theta\) indicates that the graph will have 5 petals. 2. **Equation b: \( r = 2 \sin(\theta) \)** - This is a circle in the polar coordinate system centered on the vertical axis passing through the pole. It has a radius of 1 unit. 3. **Equation c: \( r = 1 - \cos(\theta) \)** - This describes a cardioid, a heart-shaped curve that passes through the pole. When plotting these graphs, consider the domains and follow the curves as \(\theta\) varies from \(0\) to \(2\pi\). Make sure to label important points and axes to aid in the understanding of these polar graphs.
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