Answer:
(3√2, 135°) or in radians: (3√2, 3π/4)
Step-by-step explanation:
Recall that for a Cartesian (rectangular) coordinate (x,y)
this can be expressed as a polar coordinate (r,θ) where:
r = √(x² + y²)
and
tan θ = y/x
in our case, x = -3 and y = 3
r = √(x² + y²)
r = √((-3)² + 3²)
r = √(9 + 9)
r = √18 = 3√2
also
tan θ = y/x = 3/(-3) = -1
θ = -45°
however, because θ needs to be measured from the first quadrant in a positive counterclockwise sense, we need to modify θ = -45° to reflect as such.
we notice that the point (-3,3) is in the second quadrant, hence measured counterclockwise from first quadrant,
θ = 180°-45° = 135° (= 3π/4 radians)
thus we can assemble the polar coordiante
P = (r, θ) = (3√2, 135°) [ or in radians: (3√2, 3π/4) ]
