11-1!

~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)

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Ex.1: Give the rectangular coordinates for (3,30)

~First plug the point into the formulas.

y=3sin30

x=3cos30

~Now either use the trig chart or the unit circle to solve these equations.

y=3(1/2)

x=3(sqrt3/2)

~Multiply the equations.

y=1.5

x=3sqrt3/2

~Put in point form.

(3sqrt3/2,1.5)

Ex.2: Find the polar coordinates of (3,4)

~First plug into the formulas.

r=sqrt3^2+4^2

y=tan^-1(4/3)

~Solve the two equations.

r=5

y=53.13,126.87

~Put into two points.

(5,53.13)

(-5,126.87)