11-1

This week we are learning chapter 11. Chapter 11-1 is converting from polar to rectangular and converting from rectangular to polar. Also you will have to know how to plot the point in polar. I am going to show you how to do this, and give you some example problems and formulas.

FORMULAS:
(r, theta) is polar
(x,y) is rectangular

x=rcos(theta) and y=rsin(theta) is when you are converting to rectangular
r= +/-squareroot(x^2+y^2) and tan(theta) which is y/x is converting into polar

EXAMPLES:
Polar:
Give the polar point for (1,2) and plot the point in polar.
r=squareroot(1^2+2^2)
+/-5 which is going to be your first point, the x point
tan(theta)= 2/1
theta=tan^-1(2)
theta= 63.435
tan is postive in quadrants 1 and 3
Q1(5, 63.435)
Q3(5, 243.435)
To plot the polar point you just draw a number line go to 5(your x) and then do a unit circle of about how much you think 63.435 is and you do the same for the second quadrant.

Rectangular:
Give the rectangular coordinates for the point (4, 45degrees)
x=4cos45
y=4sin45
(2squareroot(2), 2squareroot(2))