Unit 4 Parametric and Polar Coordinates: Official Finals Review Guide

Understanding Parametric Equations

Purpose of Using Parametric Equations

Parametric Functions

Parametrics of Conics

Parametric Motion

Polar Coordinates Quick Review

While standard algebraic equations are written in xy form, polar equations are in terms of r (radius) and θ.

Rather than a standard coordinate plane, the polar plane is usually thought of as a circular plane. Like a standard unit circle, angles begin at the positive x axis and rotate counter-clockwise.

Domain and range are written in terms of angle measurements. For example, in the picture above the domain is 0≤θ≤2π, because the angle begins at 0 and rotates 360°, or 2π radians.

Points on the Polar Plane

Points on the polar plane are written in (r,θ) form. In the example to the left, the point is colinear to a circle with a radius of 2, so the r value is '2.' The point is rotated π/4 radians about the pole (origin of the polar plane, making the θ value 'π/4.' Keep in mind that the point (2,π/4) is the same as (-2,5π/4), because points can be written in multiple ways on the polar plane.

Trig Values in Polar Equations

To the left is a table showing points in the equation r=sinθ.

When we graph these points, we see that it creates a circle with a radius of 1 just above the x axis.

When we graph the equation on Desmos, we get the same result. Since cosθ=sin(θ-π/2), we can conclude that the graph for r=cosθ would be identical to the prior, but rotated -π/2 radians.

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