Lesson 8-1: Polar Coordinates

Graph each point. a. A(2, 45°)

• A point 2 units from the origin at a 45° angle

• A point 2 units from the origin at a 90° angle

• A point 45 units from the origin at a 2° angle

• A point 45 units from the origin at a 90° angle

Graph each point. b. (−1.5, 2π/3) is located in which quadrant?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Define: polar coordinate system

• A polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point (the pole) and an angle from a reference direction (the polar axis).

• A polar coordinate system is a three-dimensional system using only Cartesian coordinates.

• A polar coordinate system is a system where points are defined only by their x and y values.

• A polar coordinate system is a coordinate system that uses only angles to define a point.

Define: pole (in polar coordinates)

• The pole is the reference point from which distances are measured in a polar coordinate system. It is analogous to the origin in a rectangular coordinate system.

• The pole is the axis along which angles are measured in a polar coordinate system.

• The pole is the line that divides the plane into two equal halves in a polar coordinate system.

• The pole is the direction in which the radius increases in a polar coordinate system.

Define: polar axis

• The polar axis is the reference direction from which angles are measured in a polar coordinate system. It is usually a ray starting at the pole.

• The polar axis is the line joining the foci of an ellipse.

• The polar axis is the axis about which a circle rotates.

• The polar axis is the vertical line passing through the origin in a Cartesian plane.

Define: polar coordinates

• Polar coordinates are a pair of numbers (r, θ) that specify the position of a point in a plane, where r is the distance from the pole and θ is the angle from the polar axis.

• Polar coordinates are a pair of numbers (x, y) that specify the position of a point in a plane using only horizontal and vertical distances.

• Polar coordinates are a system that uses only angles to specify the position of a point in three-dimensional space.

• Polar coordinates are a pair of numbers (r, θ) that specify the position of a point on a sphere, where r is the radius of the sphere and θ is the latitude.

Define: polar equation

Define: polar graph

• A polar graph is a graph of a polar equation, showing the relationship between r and θ in the polar coordinate system.

• A polar graph is a bar graph used to compare different categories.

• A polar graph is a type of graph that only uses Cartesian coordinates.

• A polar graph is a graph that shows the relationship between time and temperature.

Graph each point.
1A. What are the coordinates of point D?

• (-1, π/2)

• (1, π/2)

• (-1, -π/2)

• (1, -π/2)

Graph each point.
1B. What are the rectangular coordinates of E(2.5, 240°)?

• (-1.25, -2.165)

• (1.25, 2.165)

• (2.5, 0)

• (-2.5, 0)