Question

What is the polar form of `( 5,14 )`?

Answer 1

`(sqrt221 , 1.23 )`

Explanation:

Using the formulae that link Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`• theta = tan^-1 (y/x)`

The point (5 , 14 ) is in the 1st quadrant and care must be taken

to ensure that `theta color(black)( " is in the 1st quadrant")`

(here x = 5 and y = 14)

`r^2 = 5^2 + 14^2 = 25 + 196 = 221 rArr r = sqrt221`

and `theta = tan^-1 (14/5 ) =1.23 color(black)(" radians ")`

and `theta color(black)(" is in the 1st quadrant")`

Polar coordinates are therefore (`sqrt221 , 1.23 )`

Answer 2

`sqrt221/_70,3^@`

Explanation:

Rectangular form `(x,y)` can be converted into polar form `(r,theta)` as follows :

`r=sqrt(x^2+y^2) and theta= tan^(-1)(y/x)`

So in this particular case we get

`r=sqrt(5^2+14^2)=sqrt221`

`theta=tan^(-1)(14/5)=70,3^@`