Objective: Test for symmetry in polar equations.

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Checking an equation for symmetry

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Presentation transcript:

Objective: Test for symmetry in polar equations. Warm up 1. Convert to rectangular equations. Identify the type of graph. a. b.

c.

2. Convert to polar equations. Identify the type of graph. a. b. c.

Example 1 Given the point : a. Find a point symmetric w.r.t x-axis (polar axis). b. Find a point symmetric w.r.t. y-axis ( ). c. Find a point symmetric w.r.t origin.

To prove symmetry: X-axis (polar axis): replace with To prove symmetry: X-axis (polar axis): replace with . Y-axis ( ): replace with ( ) . Origin (pole) : replace r with – r or replace with . Example 2 Show that the graph of is symmetry with respect to the polar axis.

Example 3 Prove that the graph of is symmetric with respect to the y-axis. Example 4 Prove that the graph of is symmetric with respect to the origin.

Classwork Pg 673 #49-56; 59-72 Pg 683 #7-12 Carnegie Learning 14.3

Homework Check Period 2