Section 12.5 - The Polar Coordinate System 12.1. The keys……

Slides:

Advertisements

Similar presentations

Advertisements

10.3 Polar Coordinates.

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

8 Complex Numbers, Polar Equations, and Parametric Equations

9.3 Polar and Rectangular Coordinates. The following relationships exist between Polar Coordinates (r,  ) and Rectangular Coordinates (x, y): Polar vs.

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.

10.2 Polar Equations and Graphs

Section 6.4 Use point plotting to graph polar equations.

7.4 Polar Coordinates and Graphs Mon March 2 Do Now Evaluate.

9.2 Graphs of Polar Eqs. Circle: radius a; center at (a, 0) in rectangular coordinates. Circle: radius a; center at (-a, 0) in rectangular coordinates.

Section 11.3 Polar Coordinates.

P OLAR E QUATIONS Section Polar Coordinates Given: r: Directed distance from the Polar axis (pole) to point P Ɵ: Directed angle from the Polar axis.

9.2 Polar Equations and Graphs. Steps for Converting Equations from Rectangular to Polar form and vice versa Four critical equivalents to keep in mind.

Polar Form and Complex Numbers. In a rectangular coordinate system, There is an x and a y-axis. In polar coordinates, there is one axis, called the polar.

When trying to figure out the graphs of polar equations we can convert them to rectangular equations particularly if we recognize the graph in rectangular.

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.

Section 12.6 – Area and Arclength in Polar Coordinates

Section 8.3 Area and Arc Length in Polar Coordinates.

REVIEW Polar Coordinates and Equations.

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

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.

1.4 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for.

CHAPTER 10 CONICS AND POLAR COORDINATES The Parabola In a plane with line, l, (directrix) and fixed point F (focus), eccentricity is defined as.

REVIEW Polar Coordinates and Equations. You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate.

Section 9.1 Polar Coordinates. x OriginPole Polar axis.

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

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.

Copyright © 2013, 2009, 2005 Pearson Education, Inc Complex Numbers, Polar Equations, and Parametric Equations Copyright © 2013, 2009, 2005 Pearson.

Polar Coordinates Lesson Points on a Plane Rectangular coordinate system  Represent a point by two distances from the origin  Horizontal dist,

1 8.7 Trigonometric Equations (I) In this section, we will study the following topics: o Solving equations involving a single trig function algebraically.

Jeopardy! for the Classroom. Real Numbers Complex Numbers Polar Equations Polar Graphs Operations w/ Complex Numbers C & V

10.7 Polar Graphs Graph Polar Equations.

10. 4 Polar Coordinates and Polar Graphs 10

Polar Equations M 140 Precalculus V. J. Motto. Graphing Polar Equations It is expected that you will be using a calculator to sketch a polar graph. Before.

Chapter 17 Section 17.4 The Double Integral as the Limit of a Riemann Sum; Polar Coordinates.

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

An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists of all points whose polar coordinates.

Polar Coordinates Lesson 6.3. Points on a Plane Rectangular coordinate system  Represent a point by two distances from the origin  Horizontal dist,

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

Section The Polar Coordinate System.

Bellwork Convert to rectangular coordinates: Convert to polar coordinates:

8. Polar Coordinates I am the polar curve r = sin(2^t)-1.7.

Ch. 11 – Parametric, Vector, and Polar Functions 11.3 – Polar Functions.

8.2 - Graphing Polar Equations

Warm Up—begin after the Quiz

Lecture 31 – Conic Sections

Graphs of Polar Equations

6.5 Graphs of Polar Equations

Parametric Equations and Polar Coordinates

Horizontal Line Test.

5.4 Graphs of Polar Equations

Section 3.2 – Polar Equations

8.2 Polar Equations and Graphs

Other Types of Polar Graphs…

Polar Coordinates and Polar Graphs

Area Between Polar Curves

Graphing Polar Equations

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.

Graphing Polar Equations

15.4 Double Integrals in Polar Form

Section 6.4 Graphs of Polar Equations

Graphing Radical Functions.

Graphs and Polar Equations

How to describe all sections of the graph

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

Presentation transcript:

Section The Polar Coordinate System 12.1

The keys……

Four Translations Point - Polar to Rectangular Point - Rectangular to Polar Equation - Polar to Rectangular Equation - Rectangular to Polar

Point – Polar to Rectangular

Point – Rectangular to Polar

Equation - Polar to Rectangular

Equation - Rectangular to Polar

Shapes of Polar Curves Graphing Polar Curves on Calculator Finding Points of Intersection (Boundaries of Integration)

The Shapes Lines Circles Cardioid Lemniscate Sprial Rose Curves

The Shapes - Lines Vertical Line Horizontal Line General Line

The Shapes - Circles

The Shapes – Cardioids (Hearts) Note: Extra loop Only if b > a

The Shapes – Lemniscates (Propellers)

The Shapes - Spirals

The Shapes – Rose Curves n even – 2n pedals n odd – n pedals

Graphing Polar Curves on Calculator 1. Change mode to Polar 2. Hit y = (you’ll see r = indicating polar mode) 3. Enter the equation 4.Graphing once should give you a sense of how to change the x, y and theta constraints.

5. Now change the constraints in WINDOW

Finding Points of Intersection (Boundaries of Integration)

WRONG ANSWER