   Chapter 10.3, Problem 38E

Chapter
Section
Textbook Problem

# Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.38. r = 2 sin 6θ

To determine

To sketch: The curves for the polar equation r=2sin6θ and its Cartesian coordinates.

Explanation

Given:

The polar equation is as below.

r=2sin6θ .

Calculation:

Substitute (0) for θ in equation r=2sin6θ .

r=2sin6θ=2sin6(0)=0

For the polar equation r=2sin6θ values for the Cartesian coordinates curve is tabulated below.

 t r 0 0 0.087305556 0.996596 0.174611111 1.7061753 0.261916667 1.9317905 0.349222222 1.6266204

Graph:

The curve for the Cartesian coordinates is shown below in figure 1.

From the figure 1 , when θ increases from 0 to π12 , the polar curve r increases from 0 to 2 in polar graph.

When θ increases from π12 to π6 , the polar curve r decreases from 2 to 0 .

When θ increases from π6 to π4 , the polar curve r decreases from 0 to 2

When θ increases from π4 to π3 , the polar curve r increases from 2 to 0 .

When θ increases from π3 to 5π12 , the polar curve r increases from 0 to 2 .

When θ increases from 5π12 to π2 , the polar curve r decreases from 2 to 0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 516, evaluate the given quantity. log1616

Finite Mathematics and Applied Calculus (MindTap Course List)

#### For y = sin 6x, dydx=. a) cos 6x b) 6 cos x c) cos 6 d) 6 cos 6x

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Graph each hyperbola. 4x23y2=36

College Algebra (MindTap Course List) 