Understanding Polar Coordinates

The video tutorial introduces the polar coordinate system, explaining how it differs from the Cartesian system by using a fixed point (the pole) and a rotational angle. It covers how to graph points using polar coordinates, detailing the concepts of radius and angle of rotation. The tutorial also explains positive and negative rotations and provides practice examples for plotting points. Additionally, it explores multiple representations of polar points, demonstrating how a single point can be expressed in various ways using different combinations of positive and negative radii and angles.

What is the fixed point in the polar coordinate system called?

• Center

• Pole

• Axis

• Origin

In polar coordinates, what does 'r' represent?

• Angle of rotation

• Distance from the pole

• X-coordinate

• Y-coordinate

How do you determine the direction of rotation for a positive angle in polar coordinates?

• Away from the pole

• Clockwise

• Counterclockwise

• Towards the pole

If a point has a negative angle in polar coordinates, which direction do you rotate?

• Counterclockwise

• Away from the pole

• Clockwise

• Towards the pole

What is the polar coordinate representation of a point with a radius of 4 and a negative rotation of π/6?

• (4, 11π/6)

• (4, π/6)

• (4, -π/6)

• (4, 5π/6)

How many different representations can a point have in polar coordinates?

• One

• Three

• Two

• Four

What happens when you have a negative radius in polar coordinates?

• Move to the right

• Move to the left

• Rotate clockwise

• Rotate counterclockwise

Which of the following is a correct representation of a point with a positive radius and a positive rotation?

• (-3, 5π/4)

• (3, 5π/4)

• (3, -5π/4)

• (-3, -5π/4)

If a point is represented as (2, -5π/6), what is its equivalent with a positive rotation?

• (2, π/6)

• (2, 11π/6)

• (2, 5π/6)

• (2, 7π/6)

What is the equivalent positive rotation for a point with a negative rotation of -7π/4?

• 7π/4

• 5π/4

• 3π/4

• π/4