Polar Coordinates and Equations

Polar Coordinates and Equations

An Introduction

Polar Coordriantes

An Introduction

Polar Coordinates

Plotting Points Using Polar Coordinates Polar-Rectangular Point Conversions Drawing Polar Graphs Converting Equations from Polar to Rectangular Converting Equations from Rectangular to Polar Polar Graph Points of Intersection More Practice

Polar coordinates

The ordered pairs, called polar coordinates, are in the form (r,θ), with r being the number of units from the origin or pole (if r>0

), like a radius of a circle, and θ being the angle (in degrees or radians) formed by the ray on the positive x–axis (polar axis), going counter-clockwise. If r<0

, the point is  units (like a radius) in the opposite direction (across the origin or pole) of the angle θ. If θ<0, you go clockwise with the angle, starting with the positive x

–axis.To plot a point, you typically circle around the positive x–axis θ

 degrees first, and then go out from the origin or pole r units (if r is negative, go the other way (180°) r units).

Here a polar graph with some points on it. Note that we typically count in increments of 15°, or π12

.

Multiple Choice

Which point represents (3, 3π/4)

• F
• E
• B
• A

Multiple Choice

Covert the rectangular equation to polar form  $y=x^2$  

• r = cot θ csc θ

• r = tan θ csc θ

• r = tan θ sec θ

• r = 0

Multiple Choice

Covert the rectangular equation to polar form  $x^2+y^2=9$  

• r² = 81

• r = 3

• r = 4.5

• r sin θ = 9

Multiple Choice

Convert the polar coordinates to rectangular form  $\left(\sqrt{2},\ -\frac{\pi}{4}\right)$  

• (1, 1)

• (1, -1) 

• (-1, 0)

• (-1, -1)

Multiple Choice

Which quadrant contains the point named by (2, 5)?

• Quadrant I
• Quadrant II
• Quadrant III
• Quadrant IV