Objective: Test for symmetry in polar equations.

Slides:

Advertisements

Similar presentations

Checking an equation for symmetry

Advertisements

WARM UP Zeros: Domain: Range: Relative Maximum: Relative Minimum:

Chapter 8 – Polar Coordinates and Parametric Equations Graphs of Polar Equations1.

Graphs of Polar Coordinates Sections 6.4. Objectives Use point plotting to graph polar equations. Use symmetry to graph polar equations.

Section 6.4 Use point plotting to graph polar equations.

Symmetries of Graphs of Equations in x and y

Polar Coordinates and Graphs of Polar Equations Digital Lesson.

Symmetry in Graphs of Polar Equations On to Sec. 6.5a!!!

Chapter 6 Additional Topics in Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Graphs of Polar Equations.

Section 1.1 GRAPHS OF EQUATIONS. List the graphs that you are able to draw:  Linear functions  Quadratic functions  Rational functions  Radical functions.

Algebra 1B Chapter 9 Solving Quadratic Equations By Graphing.

3.1 Symmetry; Graphing Key Equations. Symmetry A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point.

Objective: Identify even or odd functions. Warm up a.Describe where is the function increasing, decreasing or constant. b.What is the relative maximum?

Example: The graph of x = | y | – 2 shown below, is symmetric to x-axis y x 1 2 –323 A graph is symmetric to x- axis if whenever (x, y) is on graph, so.

Section 1.2 Graphs of Equations in Two Variables.

Symmetry Two points, P and P ₁, are symmetric with respect to line l when they are the same distance from l, measured along a perpendicular line to l.

Determine if the following point is on the graph of the equation. 2x – y = 6; (2, 3) Step 1: Plug the given points into the given equation. 2(2) – (3)

Chapter 2 Section 2.7 Graphing Techniques. Multiplying the Function or the Independent Variable by a Number.

Test an Equation for Symmetry Graph Key Equations Section 1.2.

Sullivan Algebra and Trigonometry: Section 10.2 Objectives of this Section Graph and Identify Polar Equations by Converting to Rectangular Coordinates.

Objective: Graph limacon curves. Warm up 1.Graph. a. b.

Warm – up #2. Homework Log Thurs 11/19 Lesson 4 – 2 Learning Objective: To determine symmetry & graph by translation Hw: #403 Pg. 228 #1 – 35 odd.

Do now Solve 4x 4 -65x (3, ∞) Write as an inequality Sketch Bound or unbound?

Graphing Polar Graphs Calc AB- Section10.6A. Symmetry Tests for Polar Graphs 1.Symmetry about the x -axis: If the point lies on the graph, the point ________.

Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.

Warm – up #3 1. Test for Symmetry: xy = 4 y–axis(–x)(y) = 4 NO! x–axis(x)(–y) = 4 NO! Origin(–x)(–y) = 4 YES! So it’s symmetric about the origin  –xy.

Notes Over 1.1 Checking for Symmetry Check for symmetry with respect to both axis and the origin. To check for y-axis symmetry replace x with  x. Sym.

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Polar Coordinates and Graphs of Polar Equations. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The polar coordinate system is formed.

9.7 Graphs of Polar Equations Digital Lesson. HWQ Convert the polar equation to rectangular form. Give the equation in standard form. Copyright © by Houghton.

Objective: Graph and analyze rose curves. Warm up 1.Plot point. a.Find point symmetric w.r.t. polar axis. b.Find point symmetric w.r.t.. c.Find point symmetric.

1.1) RECTANGULAR COORDINATES Pg 9 # 1- Do Now!. Coordinate Plane  Label: x, y-axis, origin, quadrants  Plot points.

Section 2.4. X-axis: replace y with –y. Simplify. If you get an equation = to what you started with, the function is symmetric to the x-axis. Y-axis:

1.1 Graph of Equations How to sketch graphs

2.1Intercepts;Symmetry;Graphing Key Equations

2.2 Graphs of Equations.

Graphs of Equations in Two Variables

Find the missing coordinate in the ordered pair

WARM UP Use the graph of to sketch the graph of

Section 6.4 Graphs of Polar Equations

11.2 Polar Equations and Graphs

Chapter 2: Functions, Equations, and Graphs

Intercepts, Symmetry, Even/Odd and intersections

Graphs of Equations In Two Variables; Intercepts; Symmetry

5.4 Graphs of Polar Equations

Sullivan Algebra and Trigonometry: Section 2.2

8.2 Polar Equations and Graphs

Symmetry and Coordinate Graphs Section 3-1

Notes Over 1.1 To check for y-axis symmetry replace x with -x.

Warm up 1) Graph.

P.1 Graphs and Models.

4.3 Symmetry Which graph is NOT a function?

Chapter 3 – The Nature of Graphs

Graphs of Equations Objectives: Find intercepts from a Graph

(Please have your homework out)

1.3 Symmetry; Graphing Key Equations; Circles

Graphs and Graphing Utilities

Section 1.2 Intercepts; Symmetry; Graphing Key Equations

Worksheet KEY 1) {0, 2} 2) {–1/2} 3) No 4) Yes 5) 6) 7) k = 1 8)

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Section 1.2 Intercepts; Symmetry;

P.1 Graphs and Models.

Chapter 2 More on Functions.

Graphs and Polar Equations

Graphs of Equations Objectives: Find intercepts from a Graph

Graphing Key Equations

Classify functions as even or odd.

P.3 Graphs of Equations (Part 4).

Objective: Test for symmetry in polar equations.

Presentation transcript:

Objective: Test for symmetry in polar equations. Warm up 1. 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 1 Show that the graph of is symmetry with respect to the polar axis.

Example 2 Prove that the graph of is symmetric with respect to the y-axis. Example 3 Prove that the graph of is symmetric with respect to the origin.

Assignment Pg 683 #7-12

Homework Check Period 2