Learning Resources

Investigation 4: Converting Between Rectangular Form and Polar Form

Converting rectangular coordinates to polar coordinates:

• You want to change the rectangular coordinate (x, y) into the polar coordinate (r, ).
• Find the radius, r, using the Pythagorean Theorem; .
• Find the reference, or related, angle using the tangent ratio.
• Find the angle by determining the quadrant in which the terminal arm is located, and making use of the reference angle.
• If the terminal arm is in the first quadrant, = the value of the reference angle.
• If the terminal arm is in the second quadrant, = 180° - reference angle.
• If the terminal arm is in the third quadrant, = 180° + reference angle.
• If the terminal arm is in the fourth quadrant,  = 360° - reference angle.