11-1

11-1 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)
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Ex.1: Give the rectangular coordinates for (4,60)
You plug these numbers into the formula
y=4sin60
x=4cos60
Usually you use the trig chart to figure these out,or you can use your calculator
y=4(.5)
x=4(.866)
~Multiply the equations.
y=2
x=3.464
~Put in point form.
(3.464,2)

Ex.2: Find the polar coordinates of (5,6)
Plug numbers into the formula
r= the square root of x^2 + y^2
r= the square root of 5^2 + 6^2 =7.810

y=tan^-1(6/5)
~Solve the two equations.
r=8
y=50.194
~Put into two points.
(8,50.194)
(-8,50.194)