10.8 Graphs of Polar Equations

Slides:

Advertisements

Similar presentations

Copyright © Cengage Learning. All rights reserved.

Advertisements

10.3 Polar Coordinates.

GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ.

Graphing Polar Equations

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.

Graphing in polar coordinate. Reminder (1) The following polar representations represent the same point: ( r, θ ) ( r, θ + 2n π ) ; nεZ ( - r, θ + (2n+1)π.

Polar Differentiation

10.2 Polar Equations and Graphs

10.7 Polar Coordinates Adapted by JMerrill, 2011.

Section 6.4 Use point plotting to graph polar equations.

Sec 5 Symmetry in polar coordinate. Definitions Symmetry about the Polar Axis The curve is symmetric about the polar axis ( the x-axis)if replacing the.

Polar Coordinates and Graphs of Polar Equations Digital Lesson.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 6 Applications of Trigonometric Functions.

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

10.3 Polar Functions Quick Review 5.Find dy / dx. 6.Find the slope of the curve at t = 2. 7.Find the points on the curve where the slope is zero. 8.Find.

Polar Coordinates and Graphing r = directed distance = directed angle Polar Axis O Counterclockwise from polar axis to.

1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.

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

11.1 Polar Coordinates and Graphs

10.8 Polar Equations and Graphs. An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists.

This is the graph of y = sin xo

Section 6-5 symmetry for polar graphs analyzing a polar graph finding maximum r-values rose curves limaçon curves other polar graphs.

Graphing Equations of Lines Using x- and y-Intercepts.

Section 10.8 Notes. In previous math courses as well as Pre-Calculus you have learned how to graph on the rectangular coordinate system. You first learned.

H.Melikyan/12001 Graphs of Polar Equations Dr.Hayk Melikyan Departmen of Mathematics and CS

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.

Graphing in polar coordinate

6.4 Amplitude and Period of Sine and Cosine Functions.

Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Sullivan Algebra and Trigonometry: Section 9.2 Polar Equations and Graphs Objectives of this Section Graph and Identify Polar Equations by Converting to.

Today in Precalculus Go over homework Notes: Graphs of Polar Equations Homework.

Section 5.2 – Polar Equations and Graphs. An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation.

Section 1.2 Graphs of Equations in Two Variables.

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)

Sketching a Quadratic Graph Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis,

Test an Equation for Symmetry Graph Key Equations Section 1.2.

Copyright © Cengage Learning. All rights reserved. 9 Topics in Analytic Geometry.

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.

Chapter 6-1 Graphing Quadratic Functions. Which of the following are quadratic functions?

Trig Graphing. Setting up the Trig graph: x y Lets graph y=sin(x)

Y = x 2 – 4x – 5 xy Vertex? Max or Min? Axis of Symmetry? Do Now 1)

Copyright © Cengage Learning. All rights reserved. 9.6 Graphs of Polar Equations.

10.7 Polar Graphs Graph Polar Equations.

10.6B and 10.7 Calculus of Polar Curves.

Polar Coordinates and Graphing. Objective To use polar coordinates. To graph polar equations. To graph special curves in polar coordinates.

Ch 9 Polar Coordinates and Complex numbers L9.2 Graphs of Polar equations.

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.

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.

Polar Equations and Graphs. 1. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar.

S p. 702: 1-19 odd, odd, odd. Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle)  Polar.

Plot These Points and then name each point with a positive radius.

8.2 - Graphing Polar Equations

6.5 Graphs of Polar Equations

2-5 Absolute Value Functions and Graphs

5.4 Graphs of Polar Equations

8.2 Polar Equations and Graphs

Other Types of Polar Graphs…

Unit 7.4: Graphs of Polar Equations

HW # −14 , ,18 , ,44 , Row 6 Do Now Convert the polar equation to rectangular form

HW # , ,16 , ,42 , Row 5 Do Now Convert the rectangular equation to polar form a. y = x b. xy = 4.

7.2 Graphing Polynomial Functions

HW # −17 , ,20 , ,46 , Row 1 Do Now Test for symmetry with respect to the line

Section 6.4 Graphs of Polar Equations

9.7 Graphs of Polar Equations

GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ

Presentation transcript:

10.8 Graphs of Polar Equations Limacons Rose Curves Lemnisactes

Lets Graph a Polar Equation Make a Table for r and θ

Lets Graph a Polar Equation

Symmetry of Polar Coordinates Symmetry with respect to a line Line the y-axis

Symmetry of Polar Coordinates Symmetry with respect to a line Line the x-axis

Symmetry of Polar Coordinates Symmetry with respect to a line Line the x-axis

Remember the Maximum and Minimum of Cos and Sin function? The Range of the Cos and Sin function – 1 to 1 The Max. of r = 4Cosθ would be r = 4(1) = 4 The Min. or r = 4Cosθ r = 4( -1) = - 4

Remember the Zero of Cos and Sin function? Zeros for

Special Polar Graphs Limacons

Special Polar Graphs Limacons

Special Polar Graphs Circles

Special Polar Graphs Rose Curves

Special Polar Graphs Lemniscates

A website to Play with Polar graphing http://www.mathdemos.org/mathdemos/family_of_functions/rose_sine_vary_a.mov

Homework Page 762 – # 1, 3, 6, 7, 13, 17, 23, 29, 35, 45, 51, 55, 65

Homework Page 762 – # 4, 8, 12, 14, 22, 30, 34