Chapter 10: Polar Coordinates; Vectors

Polar Coordinates

(r,theta)

Two Common Techniques for Transforming an Equation From Polar Form to Rectangular Form

1. Multiplying both sides of the equation by r 2. Squaring both sides of the equation

Steps for Converting from Rectangular to Polar Coordinates

1. Plot point (x,y) 2. If x=0 or y=0, use graph to determine (r, theta) 3. If x is not equal to 0 and y is not equal to zero, then r^2 = x^2 + y^2 4. To find theta, determine the quadrant: Quad I or IV: inverse tangent of y/x Quad II or III: pi + inverse tangent of y/x

Pole

A point on the polar coordinate system

Polar Axis

A ray with a vertex at the pole

Converting Rectangular Coordinates to Polar Coordinates (r)

r^2 = x^2 + y^2

Converting Rectangular Coordinates to Polar Coordinates (theta)

tan theta = y/x

Convert Polar Coordinates to Rectangular Coordinates (X)

x=r cos theta

Convert Polar Coordinates to Rectangular Coordinates (Y)

y=r sin theta