Question 1

Given the polar equation $$r = 3 + 2\cos(	heta)$$, which type of curve does this equation represent?

Accepted Answer

A limaçon without an inner loop

Question 2

For the polar equation $$r = 3 + 2\cos(	heta)$$, what is the maximum value of $$r$$?

Accepted Answer

$$r_{max} = 5$$

Question 3

Which of the following is the correct Cartesian form for the polar equation $$r = 3 + 2\cos(	heta)$$?

Accepted Answer

$$x^2$$ + $$y^2 = 3 + 2$$\frac{x}{\sqrt{$$x^2$$ + $$y^2$$}}$$

Question 4

If a point on the curve $$r = 3 + 2\cos(	heta)$$ has $$	heta = \frac{\pi}{2}$$, what is the corresponding value of $$r$$?

Accepted Answer

$$r = 3$$

Question 5

Which of the following best describes the symmetry of the graph of $$r = 3 + 2\cos(	heta)$$?

Accepted Answer

Symmetric about the $$x-$$axis

Question 6

What is the minimum value of $$r$$ for the curve $$r = 3 + 2\cos(	heta)$$?

Accepted Answer

$$r_{min} = 1$$

Question 7

Which of the following points lies on the curve $$r = 3 + 2\cos(	heta)$$ when $$	heta = 0$$?

Accepted Answer

$$(5, 0)$$

Question 8

If $$r = 3 + 2\cos(	heta)$$, what is the value of $$r$$ when $$	heta = \pi$$?

Accepted Answer

$$r = 1$$

Question 9

Which transformation would change the equation $$r = 3 + 2\cos(	heta) to$$ $$r = 3 + 2\sin(	heta)$$?

Accepted Answer

Rotate the graph $$90^\circ$$ counterclockwise

Question 10

A real-world application: A radio antenna emits signals in a pattern described by $$r = 3 + 2\cos(	heta). $$What is the farthest distance a signal can reach from the antenna?

Accepted Answer

$$5$$ units

Question 11

Which of the following statements is true about the graph of $$r = 3 + 2\cos(	heta)$$?

Accepted Answer

It has a dimple but no inner loop

Question 12

If the equation $$r = 3 + 2\cos(	heta) is $$graphed, what is the $$r-$$intercept (where $$	heta = 0$$)?

Accepted Answer

$$r = 5$$

Question 13

Which of the following best describes the shape of the graph for $$r = 3 + 2\cos(	heta)$$?

Accepted Answer

Limaçon with a dimple

Question 14

If $$r = 3 + 2\cos(	heta)$$, what is the value of $$r$$ when $$	heta = \frac{3\pi}{2}$$?

Accepted Answer

$$r = 3$$

Question 15

Which of the following is a general form for a limaçon curve?

Accepted Answer

$$r = a + b\cos(	heta)$$

Graphing Curves Using Polar Equations

Study Guide - Practice Questions

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