Find all points of tangency? ) Uhe ogrophing utility polar equation.Usetograph the7.r=3 sin o cOSeFind all pgints of horizontal tangencg. CRound gourgouansuer )tofour decimal plo es.

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Description: Find all points of tangency? ) Uhe ogrophing utility polar equation.Usetograph the7.r=3 sin o cOSeFind all pgints of horizontal tangencg. CRound gourgouansuer )tofour decimal plo es.

Given Polar equation, r = 3sinθcos2θ, 0≤θ<2π We know that for horizontal tangent the slope of…

Answered: ) Uhe ogrophing utility polar equation.…

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.

Expert Solution

Step 1

Given Polar equation,

$r = 3 \sin (θ) \cos^{2} (θ), 0 \leq θ < 2 π$

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

i.e. $\frac{d y}{d x} = 0$

The derivative of the polar curve is given by

$\frac{dy}{dx} = \frac{\frac{d r}{d θ} \sin (θ) + r \cos (θ)}{\frac{d r}{d θ} \cos (θ) - r \sin (θ)}$

Used differentiation formulas:

$\frac{d}{d x} x^{n} = n x^{n - 1} \frac{d}{d θ} \sin (θ) = \cos (θ) \frac{d}{d θ} \cos (θ) = - \sin (θ)$

Product rule of differentiation:

$\frac{d}{d x} (f (x) \cdot g (x)) = f' (x) g (x) + f (x) g' (x)$

Chain rule of differentiation:

$\frac{d}{d x} (f (g (x))) = f' (g (x)) \cdot g' (x)$

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