Question

What is the polar form of `( -7,1 )`?

Answer 1

`(5sqrt2 , 3 )`

Explanation:

Use the following formulae linking Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`• theta = tan^-1 (y/x )`

[( - 7 , 1 ) is a point in the 2nd quadrant and care must be taken

to ensure that `theta` , is in the 2nd quadrant.]

so `r^2 = (-7)^2 + 1^2 = 49 + 1 = 50 rArr r =sqrt50 = 5sqrt2`

and `theta = tan^-1 =(1/-7 ) = - 0.14color(black)("radians")`

`rArr theta = ( pi - 0.14 ) = 3 color(black)("radians" )`