) Uhe ogrophing utility polar equation. Use tograph the 7. r=3 sin o cOSe Find all pgints of horizontal tangencg. CRound gour gou ansuer ) tofour decimal plo es.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find all points of tangency?

) Uhe ogrophing utility polar equation.
Use
tograph the
7.
r=3 sin o cOSe
Find all pgints of horizontal tangencg. CRound gour
gou
ansuer )
tofour decimal plo es.
Transcribed Image Text:) Uhe ogrophing utility polar equation. Use tograph the 7. r=3 sin o cOSe Find all pgints of horizontal tangencg. CRound gour gou ansuer ) tofour decimal plo es.
Expert Solution
Step 1

Given Polar equation,

r = 3sinθcos2θ,     0θ<2π

We know that for horizontal tangent the slope of the tangent is zero which means the derivative of the curve is 0.

i.e. dydx=0

The derivative of the polar curve is given by

dydx=drdθsinθ+rcosθdrdθcosθ-rsinθ

Used differentiation formulas:

ddxxn = nxn-1ddθsinθ = cosθddθcosθ = -sinθ

Product rule of differentiation:

ddxfx·gx = f'xgx+fxg'x

Chain rule of differentiation:

ddxfgx = f'gx·g'x

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