How do you find the polar coordinates given (2,23)?

1 Answer
Nov 17, 2016

Please see the explanation.

Explanation:

Polar coordinates are an order pair of (r,θ)

The conversion from (x,y) to r is:

r=x2+y2

The conversion from (x,y) to θ is more complicated:

If x>0andy0, then θ=tan1(yx) [1]

If x=0andy>0, then θ=π2 [2]

If x=0andy<0, then θ=3π2 [3]

If x<0, then θ=π+tan1(yx) [4]

If x>0andy<0, then θ=2π+tan1(yx) [5]

For the given point (2,23)

r=(2)2+(23)2

r=4+12

r=16

r=4

Because the x coordinate is less than zero, we use equation [4]:

θ=π+tan1(232)

θ=π+π3

θ=4π3

The polar point is (4,4π3)