Question

What is the Cartesian form of `( 4 , ( 11pi)/4 )`?

Answer 1

`(-2sqrt2 , 2sqrt2 )`

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

`• x = rcostheta`

`• y = rsintheta`

here r = 4 and `theta = (11pi)/4`
`"---------------------------------------------------"`
`rArr x = 4cos((11pi)/4) = 4cos((11pi)/4 - 2pi) = cos((3pi)/4)`

and `cos((3pi)/4) = -cos(pi/4) = - 1/sqrt2`
thus `x = 4xx(-1)/sqrt2 = - 2sqrt2`
`"-------------------------------------------------"`

`rArr y = 4sin((11pi)/4) = 4sin(pi/4) = 4xx1/sqrt2 = 2sqrt2`