Find the polar coordinates of (8, –8) for r > 0.
r^2 = 64+64 = 128
r = 8√2
(8,-8) is in IV and tanØ=-1
Ø = 315° or 7π/4
(x,y) ----> (r,Ø)
(8,-8) ---> (8√2 , 7π/4)
To find the polar coordinates of a point such as (8, -8), we can use the following formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y/x)
Using the given point (8, -8), we can substitute the values into the formulas:
r = sqrt(8^2 + (-8)^2) = sqrt(64 + 64) = sqrt(128) = 8√2
θ = arctan((-8)/8) = arctan(-1) = -45 degrees
Therefore, the polar coordinates for (8, -8) in the case of r > 0 are (8√2, -45°).