(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

Slides:

Advertisements

Similar presentations

Polar Coordinates We Live on a Sphere.

Advertisements

Cylindrical and Spherical Coordinates

6/4/13 Obj: SWBAT plot polar coordinates

In this section, we will study the following topics:

Polar Coordinate System 11.3 – Polar Coordinates Used to plot and analyze equations of conics (circles, parabolas, ellipses, and hyperbolas. Another method.

Polar Coordinate System You are already familiar with the Rectangular Coordinate System.

8 Complex Numbers, Polar Equations, and Parametric Equations

Using Polar Coordinates Graphing and converting polar and rectangular coordinates.

Converting Between Rectangular and Polar Coordinates Sometimes we want to change from rectangular coordinates to polar coordinates, and from polar coordinates.

10.7 Polar Coordinates Adapted by JMerrill, 2011.

Section 6.3 Polar Coordinates. The foundation of the polar coordinate system is a horizontal ray that extends to the right. This ray is called the polar.

(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.

Polar Coordinates and Graphs of Polar Equations Digital Lesson.

Polar Coordinates a different system of plotting points and coordinates than rectangular (x, y) it is based on the ordered pair (r, θ), where r is the.

POLAR COORDINATES (Ch )

REVIEW Polar Coordinates and Equations.

Section 6.4a: Our standard (x, y) system is called the _____________ coordinate system rectangular Today, we start learning about the P PP POLAR coordinate.

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

Intro to Polar Coordinates Objectives: Be able to graph and convert between rectangular and polar coordinates. Be able to convert between rectangular and.

Using Polar Coordinates Graphing and converting polar and rectangular coordinates.

10.4A Polar Equations Rectangular: P (x, y) Polar: P (r,  )  r = radius (distance from origin)   = angle (radians)

11.1 Polar Coordinates and Graphs

8.2.2 – Graphing Polar Points, Converting Equations.

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

Trigonometry The science of studying angle measure.

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

Polar Coordinates In this section, we will study the following topics: Converting between polar and rectangular coordinates.

(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

Copyright © 2011 Pearson, Inc. 6.4 Polar Coordinates.

Polar Coordinates Packet 1. Polar Coordinates  Recording the position of an object using the distance from a fixed point and an angle made from that.

Section 6.1 Radian Measure

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

Section 6.3 Polar Coordinates. Another Way of Graphing The rectangular coordinate system we regularly use is not the only means we have of graphing points.

Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY.

Unit 7: Angles and Angle Measures

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

Print polar coordinates for hw

Notes 10.7 – Polar Coordinates Rectangular Grid (Cartesian Coordinates) Polar Grid (Polar Coordinates) Origin Pole Positive X-axis Polar axis There is.

Copyright © 2011 Pearson Education, Inc. Slide Cartesian vs. Polar.

Polar Coordinates Today’s Objective: I can convert between polar coordinates/equations and rectangular coordinates/equations.

(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

Today, we start learning about the POLAR coordinate system…

11.1 Polar Coordinates.

6.4 - Polar Coordinates HW: Pg. 539 #16-26.

6.4 Polar Coordinates.

Sullivan Algebra and Trigonometry: Section 10.1

REVIEW 9.1, 9.3, and 9.4 Polar Coordinates and Equations.

Objective: Polar coordinate system. Coordinate conversion.

International Studies Charter School. Pre-Calculus Section 6-3

11.1 Polar Coordinates and Graphs

Polar Coordinates r Pole Polar axis.

Polar Coordinates.

Using Polar Coordinates

Trigonometry Second Edition Chapter 5

10.7 Polar Coordinates.

6.4 Polar Coordinates.

Unit 6: Applications of Trigonometry

Parametric Equations & Plane Curves

POLAR COORDINATES Dr. Shildneck.

6.4 Polar Coordinates.

Demana, Waits, Foley, Kennedy

Graphing Polar Coordinates

Presentation transcript:

(r,  )

You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate system.

The center of the graph is called the pole. Angles are measured from the positive x axis. Points are represented by a radius and an angle (r,  ) radiusangle To plot the point First find the angle Then move out along the terminal side 5

A negative angle would be measured clockwise like usual. To plot a point with a negative radius, find the terminal side of the angle but then measure from the pole in the negative direction of the terminal side.

Let's plot the following points: Notice unlike in the rectangular coordinate system, there are many ways to list the same point.

Let's take a point in the rectangular coordinate system and convert it to the polar coordinate system. (3, 4) r  Based on the trig you know can you see how to find r and  ? 4 3 r = 5 We'll find  in radians (5, 0.93) polar coordinates are:

Let's generalize this to find formulas for converting from rectangular to polar coordinates. (x, y) r  y x

Now let's go the other way, from polar to rectangular coordinates. Based on the trig you know can you see how to find x and y? rectangular coordinates are: 4 y x

Let's generalize the conversion from polar to rectangular coordinates. r y x

330  315  300  270  240  225  210  180  150  135  120  00 90  60  30  45  Polar coordinates can also be given with the angle in degrees. (8, 210°) (6, -120°) (-5, 300°) (-3, 540°)

Convert the rectangular coordinate system equation to a polar coordinate system equation.  r must be  3 but there is no restriction on  so consider all values. Here each r unit is 1/2 and we went out 3 and did all angles. Before we do the conversion let's look at the graph.

Convert the rectangular coordinate system equation to a polar coordinate system equation. substitute in for x and y We wouldn't recognize what this equation looked like in polar coordinates but looking at the rectangular equation we'd know it was a parabola. What are the polar conversions we found for x and y?