Question

Convert the rectangular coordinate (x, y) to a Polar coordinate, P = (r, θ): (−3, 3).

Answer 1

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)  ]