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Precalculus Examples
Step 1
Use the conversion formulas to convert from polar coordinates to rectangular coordinates.
Step 2
Substitute in the known values of and into the formulas.
Step 3
Add full rotations of until the angle is greater than or equal to and less than .
Step 4
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 5
The exact value of is .
Step 6
Step 6.1
Move the leading negative in into the numerator.
Step 6.2
Factor out of .
Step 6.3
Cancel the common factor.
Step 6.4
Rewrite the expression.
Step 7
Multiply by .
Step 8
Add full rotations of until the angle is greater than or equal to and less than .
Step 9
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 10
The exact value of is .
Step 11
Step 11.1
Factor out of .
Step 11.2
Cancel the common factor.
Step 11.3
Rewrite the expression.
Step 12
The rectangular representation of the polar point is .