Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 49RE
Related questions
Question
Graph the curve r = sin(80/5)
Expert Solution
Step 1
Given:
Equation of the curve:
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
Now find the domain for θ.
If n complete rotations are required until the curve starts to repeat itself, then
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
.
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