Question

What is the polar form of `( -27,15 )`?

Answer 1

`( sqrt954 , 2.63 )`

Explanation:

Use the following formulae that links Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`• theta = tan^-1 (y/x)`

Here x = - 27 and y = 15 .[ Note also that (-27 , 15 ) is a point in

the 2nd quadrant and so care must be taken to ensure `theta`

is in the 2nd quadrant.]

`r^2 = (-27)^2 + (15)^2 = 729 + 225 = 954`

`rArr r = sqrt954`

`theta = tan^-1 (15/-27) =- 0.51 color(black)("radians")`

To find `theta color(black)(" in the 2nd quadrant")`

`theta = ( pi - 0.51 ) =2.63 color(black)(" radians")`

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