   Chapter 10.4, Problem 67E

Chapter
Section
Textbook Problem

# Horizontal Tangency In Exercises 71 and 72, find the points of horizontal tangency to the polar curve. r = 2 csc θ + 3

To determine

To calculate: The points of horizontal tangency to the polar curve given as r=2cscθ+3.

Explanation

Given:

The given polar equation r=2cscθ+3.

Formula used:

Differentiation, ddx(cosθ)=sinθ.

Calculation:

The given equation is,

r=2cscθ+3 …… (1)

The polar equation is converted into rectangular coordinates as shown below,

x=rcosθ=(2cscθ+3)cosθ

And,

y=rsinθ=(2cscθ+3)sinθ=3sinθ+2

Differentiate the equation given as, (y=3sinθ+2) with respect to θ

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