11-1 Polar

This week we learned polar.

When using polar graphs using angles(r,theta) instead of (x,y)

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

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

**Unit circle

Example 1: Give the rectangular coordinates for each point.

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)

--Danielle