Question

How do you convert (15, -3) into polar coordinates?

Answer 1

`(sqrt234 , - 11.3^@ )`

Explanation:

To convert from Cartesian coordinates to Polar . Use the
following formulae.

`• r^2 = x^2 + y^2`

`• tantheta = (y/x)`

In this question x = 15 and y = - 3

so `r^2 = 15^2 + (- 3 )^2 = 225 + 9 = 234 rArr r = sqrt234`

and `tantheta = (-3/15) rArr theta = tan^-1 (-3/15) = - 11.3^@`

Note : ( 15 , - 3 ) is a point in the 4th quadrant and so `theta` must
be in this quadrant

Since negative angles are measured from the x-axis in a
clockwise direction then `theta = -11.3^@` is in this quadrant.