Convert the rectangular coordinates to polar coordinates, using radian measure for the angle.
(6, -6)
6√(2),7π/4 OR -6√(2),5π/4
(6,-6) is in QIV
Where are the given angles?
To convert rectangular coordinates to polar coordinates, we use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Given the rectangular coordinates (6, -6), we can calculate the polar coordinates as follows:
Step 1: Calculate r (the distance from the origin):
r = √(6^2 + (-6)^2)
= √(36 + 36)
= √72
= 6√2
Step 2: Calculate θ (the angle in radians):
θ = arctan(-6/6)
= arctan(-1)
= -π/4 (Note: arctan returns a value in the range of -π/2 to π/2)
However, the given question specifies using radian measure for the angle, so we need to convert -π/4 to a positive angle using π and the given range (-π to π).
-π/4 = -π/4 + π
= -π/4 + 4π/4
= 3π/4
Therefore, the polar coordinates are (6√2, 3π/4).