   Chapter 10.4, Problem 101E

Chapter
Section
Textbook Problem

# Rotated Curve In Exercises 101–104, use the results of Exercises 99 and 100.Write an equation for the limaçon r = 2– sin θ after it has been rotated by the given amount. Use a graphing utility to graph the rotated limaçon for (a) θ = π/4, (b) θ = π/2, (c) θ = π, and (d) θ = 3 π/2.

(a)

To determine

To graph: The limaçon, r=2sinθ when it has been rotated counterclockwise through an angle of π4.

Explanation

Given:

The equation of a limaçon, r=2sinθ and an angle through which the limaçon is rotated in the anti-clock wise direction, π4.

Formula used:

When the polar curve r=f(θ) is rotated about the pole through an angle of ϕ, then the equation of the rotated curve is, r=f(θϕ).

Graph:

Consider the equation of the limaçon, r=2sinθ.

Now, the given limaçon is rotated at an angle in the anti-clock wise direction by, π4

(b)

To determine

To graph: The limaçon, r=2sinθ when it has been rotated counterclockwise through an angle of π2.

(c)

To determine

To graph: The limaçon, r=2sinθ when it has been rotated counterclockwise through an angle of π.

(d)

To determine

To graph: The limaçon, r=2sinθ when it has been rotated counterclockwise through an angle of 3π2.

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