Polar Equations and Their Graphs

This video tutorial explores the graphs of various polar equations, including R = Cosine Theta, R = Sin 2 Theta, R = Cosine 3 Theta, and R = 1 + Sin Theta. It explains how these graphs are traced as Theta increases from 0 to 2 pi radians, highlighting the unique shapes and patterns formed by each equation. The tutorial also showcases some interesting and visually appealing polar graphs, demonstrating the creative potential of polar equations.

What shape is formed by the graph of R = cos(Theta)?

• Ellipse

• Circle

• Parabola

• Hyperbola

In which quadrant are points plotted when R is negative for R = cos(Theta)?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

How many petals does the graph of R = sin(2Theta) have?

• Three

• Two

• Five

• Four

When R = sin(2Theta) is negative, in which direction are points plotted?

• Same direction

• Opposite direction

• Perpendicular direction

• No direction

How many petals are present in the graph of R = cos(3Theta)?

• Three

• Two

• One

• Four

For R = cos(3Theta), in which quadrant are points plotted when R is negative?

• Fourth quadrant

• Second quadrant

• Third quadrant

• First quadrant

What special shape is formed by the graph of R = 1 + sin(Theta)?

• Ellipse

• Cardioid

• Parabola

• Hyperbola

How many radians does it take to complete the graph of R = 1 + sin(Theta)?

• Pi radians

• 2 Pi radians

• 3 Pi radians

• 4 Pi radians

Which of the following is a characteristic of the fun polar graphs shown?

• They are all ellipses

• They are all circles

• They have overlapping petals

• They are all parabolas

What is a common feature of the fun polar graphs presented?

• They are all hyperbolas

• They are all straight lines

• They are all squares

• They resemble company logos