- When dealing with polar graphs, instead of using the standard coordinatets (x,y), we use the polar coordinates (r,theta). We can convert between rectangular and polar coordinates.
- Converting from polar to rectangular: x=(r)(cos)(theta) y=(r)(sin)(theta)
- Converting from rectangular to polar: r=sq.root of (x^2 + y^2) theta = tan^-1(y/x)
Example 1: Give the polar coordinates for (5,0).
- r=sq. root of (5^2 + 0^2)
- r=+/-5
- theta=tan^-1(0/5)
- theta=0 *Now you must find where tan is 0 on the unit circle, which is at 0 and 180.
- Now, looking at the point (5,0), you see it is at the 0 degree mark, so your polar coordinates are (5,0 degrees).
Example 2: Give the rectangular coordinates for (4, 120 degrees).
- x=(4)cos(120 degrees) *Find a reference angle off 120 in order to get a value off the trig chart. You should get -60, which is -1/2.
- x=4(-1/2)
- x=-2
- y=(1)sin(120 degrees) *Find a reference angle just as you did when finding x. You should get -60, which is (sq.root of 3/2).
- y=4((sq.root of 3)/2)
- Your rectangular coordinates are (-2,(sq.root of 3)/2).
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