3.5 Describing how angles and radii change with respect to each other in a polar graph

• In polar coordinates, the angle (θ) is measured from the positive x-axis
• In a polar graph, the angle determines the direction
• The angle in polar coordinates is measured counterclockwise from the positive x-axis.


  True
• Match the polar coordinate component with its role:

  Angle (θ) ↔️ Determines direction

  Radius (r) ↔️ Represents distance
• What happens to the point's position if the radius decreases while the angle remains constant?

  Moves closer to origin
• What role does the angle (θ) play in polar coordinates?

  Direction from x-axis
• What does a change in the radius (r) affect in polar coordinates?

  Distance from origin
• Changing θ from 0 to π/2 in polar coordinates moves the point 90° counterclockwise from the positive x-axis.


  True
• What two components are used in polar coordinates to represent a point?

  Angle and radius
• In polar coordinates, the x-coordinate is calculated as $r \cos(\theta)$


  True
• What role does the radius play in polar coordinates?

  Distance from origin
• How are polar coordinates (r, θ) converted to Cartesian coordinates (x, y)?

  $x =$$r \cos(\theta), y =$$r \sin(\theta)$
• An increase in the angle in polar coordinates moves the point counter-clockwise
• The angle (θ) in polar coordinates measures the direction from the positive x-axis.


  True
• Steps describing the effect of changing the angle (θ) while the radius (r) remains constant in polar coordinates.

  1️⃣ Increase in θ ||| Point moves counterclockwise around the circle

  2️⃣ Decrease in θ ||| Point moves clockwise around the circle
• If the radius (r) in polar coordinates increases, what happens to the point's position?

  Moves further from origin
• What does the radius (r) in polar coordinates represent?

  Distance from origin
• What happens to the point in a polar graph as the angle increases?

  Moves around the circle
• Polar coordinates use an angle and a radius
• Changing the angle in polar coordinates while keeping the radius constant moves the point around the circle.

  True
• What happens to a point in polar coordinates when the radius (r) changes while the angle (θ) remains constant?

  Moves closer or further
• The radius (r) in polar coordinates represents the distance from the origin.
• If the angle (θ) in polar coordinates increases, the point moves counterclockwise around the circle.