Polar and Rectangular!

~Rectangular Form is stated as (x,y)

~Polar Form is stated as (r,y)

To convert from polar to rectangular use the formulas:

~y=rsiny

~x=rcosy

To convert from rectangular to polar use the formulas:

~r=sqrt. x^+y^2

~y=tan^-1(y/x)

____________________________________________________________

Ex.1: Give the rectangular coordinates for (2,30)

~First plug this point into the formulas

x=2cos30

y=2sin30

~Now use either your trig chart or your calculator to solve the equation.

x=2(sqrt. 3/2)

y=2(1/2)

~Multiply out the answers

x=2sqrt.3/2

y=1

~Put your answer in point form.

(2sqrt3/2,1)

Ex.2: Give the polar coordinates for the point (2,-2)

~First plug this point into the formulas

r=sqrt. 2^2+(-2)^2

y=tan^-1(-2/2)

~Now solve the two equations.

r=+/- sqrt8

y=135, 315

~Finally put the answers into two points.

(-sqrt8, 315)

(sqrt8, 135)

~