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Description: Need help with Multivariable Question Find the area of the region in the first quadrant enclosed by onepetal of the three petal rose. The three petal rose has the polar equationr = sin(36).r= Sin(30)

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Find the area of the region in the first quadrant enclosed by one petal of the three petal rose. The three petal rose has the polar equation r = sin(30). Sa Sin (30)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 68E

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Question

Need help with Multivariable Question

Find the area of the region in the first quadrant enclosed by one
petal of the three petal rose. The three petal rose has the polar equation
r = sin(36).
r= Sin(30)

Expert Solution

Step 1

Here we have to find the area of the first quadrant enclosed by one petal of the three petal rose.

given that the polar equation of the petal rose is r = sin (3 theta)

Find the angle where the curve begins and ends. for this set r = 0, and then solve equation:

$\begin{array}{l} r = \sin 3 θ \\ \sin 3 θ = 0 \\ The general solution for \sin 3 θ = 0 \\ 3 θ = 0 + 2 π n \Rightarrow θ = \frac{2 π n}{3} \\ 3 θ = π + 2 π n \Rightarrow θ = \frac{π}{3} + \frac{2 π n}{3} \\ In first quadrand it varies from: \\ θ_{1} = 0 to θ_{2} = \frac{π}{3} \end{array}$

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