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