How can we use the concept:
Cartesian coordinates are expressed in (x, y).
Polar coordinates expressed in (r, )
To convert from polar coordinates to cartesian (or vice versa) we will use this triangle:
Sample Math Problems
Question
To convert from Cartesian coordinates to Polar:
What is (8, 4) in Polar coordinates?
Use the Pythagorean Theorem to find the hypotenuse which is r.
Answer
r = 10
Use the tangent to find the angle.
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So (8,4) in Cartesian coordinates is (10, 26.6°) in Polar Coordinates.
Question
What is (5, 13) in Polar coordinates?
Use the Pythagorean Theorem to find the hypotenuse which is r.
Answer
Question
To convert from Polar coordinates to Cartesian.
What is (12, 21.4°) in Cartesian coordinates?
Use the cosine function to find x.
Answer
cos(21.4°) =
Solve for x.
x = 12[cos(21.4°)]
x = 12(0.931)
x = 11.172
Use the sine function to find y.
sin(21.4°) =
Question
What is (7, 15.3°) in Cartesian coordinates?
Use the cosine function to find x.
Answer
cos(15.3°) =
Solve for x.
x = 7[cos(15.3°)]
x = 7(0.964)
x = 6.748
Use the sine function to find y.
sin(15.3°) =
