Polar!

I hope everyone has a great week and a Happy Thanksgivingg! :-)

Graphs using angles(r,theta) instead of (x,y)

To convert from polar to rectangular *unit circle*
x=rcostheta y=rsintheta

To convert from rectangular to polar *unit circle*
r=square root of x^2+y^2 theta=tan^-1(y/x)

Example 1:
Give polar coordinates (r,theta), where theta is in degrees, for each point.
a. (-2,2)
r=square root of 2^2+2^2
r=square root of 8
r=+/-2square root of 2
theta=tan^-1(2/-2)
theta=tan^-1(-1)
theta=135degrees and 315degrees
(2square root of 2,135degrees)
(-2square root of 2, 315degrees)

b.(5,0)
r=square root of 5^2+0^2
r=square root of 25
r=+/-5
theta=tan^-1(0/5)
theta=tan^-1(0)
theta=0degrees, 180degrees, 360degrees
(5,0)

c.(square root of 2,-square root of 2)
r=square root of the square root of 2^2+-square root of 2^2
r=square root of 2+2
r=square root of 4
r=+/-2
theta=tan^-1(-square root of 2/square root of 2)
theta=tan^-1(-1)
(2,-45)

d.(-square root of 3,1)
r=square root of the -square root of 3^2+1^2
r=square root of 3+1
r=square root of 4
r=+/-2
theta=tan^-1(1/-square root of 3)
theta=tan^-1(-square root of 3/3)
theta=150degrees and 315degrees
(2,150degrees)
(-2,315degrees)

Example 2:
Give the rectangular coordinates for each point.
a.(4,120degrees)
x=rcostheta y=rsintheta
x=4cos120degrees
x=4(1/2)
x=2
y=4sin120degrees
y=4(square root of 3/2)
y=4square root of 3/2
y=2square root of 3
(-2,2square root of 3)

b.(-3,90degrees)
x=rcostheta y=rsintheta
x=-3cos90degrees
x=-3(0)
x=0
y=-3sin90degrees
y=-3(1)
y=-3
(0,-3)

c.(1,5pi/6)
x=rcostheta y=rsintheta
x=1cos30degrees
x=1(square root of 3/2)
x=square root of 3/2
y=1sin30degrees
y=1sin(1/2)
y=1/2
(-square root of 3/2,1/2)

d.(2,3pi/4)
x=rcostheta y=rsintheta
x=2cos(3pi/4)
x=2cos(square root of 2/2)
x=2(square root of 2/2)
x=square root of 2
y=2sin45degrees
y=2sin(square root 2/2)
y=square root of 2
(-square root of 2,square root of 2)