11-1

11-1 Polar
This week I'm going to do a review on 11-1 where we learned how to convert from polar to rectangular and from rectangular to polar. In this section, we also use polar points in which we don't use (x,y) but (r,theta) instead.
-To convert from polar to rectangular: x = r(cos)(theta)    y = r(sin)(theta)
-To convert from rectangular to polar: r = square root of x^2 + y^2     theta = tan^-1(y/x)

Example 1: Give the polar coordinates for (5,0).
r = square root of 5^2 + 10^2
r = +/-5
theta = tan^-1(0/5)
theta = 0
final answer: (5,0) (-5,0)


Example 2: Give the rectangular coordinates for (3,30 degrees).
x = r(cos)(theta)
x = 3cos30
x = 3(sq. root of 3/2)
x = 3(sq. root of 3)/2
y = r(sin)(theta)
y = 3sin30
y = 3(1/2)
y = 3/2
final answer: (3(sq. root of 3)/2, 3/2)