Question

Which graph represents the polar curve r = 3 – 2cos(θ)?

Answer 1

The graph of the polar curve r = 3 – 2cos(θ) is in the attachment

What is a graph?

A graph is a diagram representation on a coordinate system.

What is a polar curve?

A polar curve is a curve represented by the equation r = a + bcosθ where

• a and b are constants and
• θ = the argument of the curve

How to find the graph of the polar curve r = 3 – 2cos(θ)?

To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.

The maximum value of r

Since r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(-1)

r = 3 + 2

r = 5

The minimum value of r

Since r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(1)

r = 3 - 2

r = 1

The value of r at the origin

Since r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2cos(π/2)

r = 3 – 2(0)

r = 3 - 0

r = 3

So, in polar form, the points we require for the polar curve graph are

• (5, π),
• (1, 0),
• (3, π/2) and
• (3, 3π/2)

Find the graph of the polar curve in the attachment

Learn more about graph of polar curve here:

brainly.com/question/26193139

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