Question

What is the polar form of `(-5,3)`?

Answer 1

`(sqrt34 , 2.6)`

Explanation:

Using the formulae that links Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`• theta = tan^-1(y/x)`

here x = - 5 and y = 3

`" hence " r^2 = (-5)^2 +3^2 = 25 + 9 = 34 rArr r = sqrt34`

Now the point (-5,3) is in the 2nd quadrant so care must be taken to ensure `theta " is in the 2nd quadrant "`

`theta = tan^-1(-3/5) = -0.54" radians "`

`rArr theta = (pi - 0.54 ) ≈ 2.6" radians "`