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The graph of the polar curve r = 3 – 2cos(θ) is in the attachment
<h3>What is a graph?</h3>A graph is a diagram representation on a coordinate system.
<h3>What is a polar curve?</h3>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
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.
<h3>The maximum value of r</h3>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
<h3>The minimum value of r</h3>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
<h3>The value of r at the origin </h3>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:
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so, we have two 54x18 rectangles, so their perimeter is simply all those units added together, 54+54+54+54+18+18+18+18 = 288.
we know the circle's diameter is 1.5 times the width, well, the width is 18, so the diameter of the circle must be 1.5*18 = 27.