Graph the curve r = sin(80/5)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 49RE
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Graph the curve r = sin(80/5)

Expert Solution
Step 1

Given:

Equation of the curve:

Calculus homework question answer, step 1, image 1

Step 2

 

To graph the function r = sin(8θ/5) convert given function in parametric form.

The polar equation  r=f(θ)  in parametric equation can be written as

x=r cosθ =f(θ)cosθ,  y=r sinθ =f(θ)sinθ

Thus the given equation can be written in parametric form as

Calculus homework question answer, step 2, image 1

Now find the domain for θ.

If n complete rotations are required until the curve starts to repeat itself, then

Calculus homework question answer, step 2, image 2

Step 3

Also it is require that 16nπ be even multiple of π.

This is possible if n=5.

The entire curve will be drawn if 0≤θ≤2πn.

That is 0≤θ≤10π.

Thus the equation need to graph is 

Calculus homework question answer, step 3, image 1.

 

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