Graphing Polar Curves Concepts

Graphing Polar Curves Concepts

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

This video tutorial explains how to graph a polar curve using the polar equation r = 1 + cos(θ), which forms a cardioid. The process begins by plotting the equation in the rectangular plane, treating r as y and θ as x. This method simplifies the graphing process by avoiding tedious value tables. The tutorial demonstrates how to use the vertical distance from the x-axis to determine the distance of polar points from the origin. Key points such as θ = 0, π/2, π, 3π/2, and 2π are plotted, and symmetry is used to complete the graph. The video concludes with a brief mention of future examples and a call to action for viewers to like and subscribe.

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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the polar equation discussed in the video?

r = sin(θ) + 1

r = 1 + cos(θ)

r = 1 + sin(θ)

r = cos(θ) - 1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What shape does the polar equation r = 1 + cos(θ) form?

Ellipse

Cardioid

Parabola

Circle

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we plot the polar equation in the x-y plane?

To avoid using polar coordinates

To simplify the graphing process

To make a table of values

To find the slope of the curve

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the x-y plane, what does 'r' represent?

z

x

y

θ

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the basic cosine graph modified to match the polar equation?

Shifted one unit up

Shifted one unit left

Shifted one unit right

Shifted one unit down

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the vertical distance from the x-axis represent in the polar graph?

The y-coordinate

The x-coordinate

The radius r

The angle θ

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

At θ = 0, what is the value of r?

0

1

2

3

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