Question

How do you find the rectangular coordinate of (sqrt 2, 315 degrees)?

Answer 1

( 1 , -1 )

Explanation:

To convert from Polar to Rectangular coordinates use :

`• x = rcostheta | y = rsintheta`

Here `r = sqrt2 , theta = 315^@`

`rArr x = sqrt2cos315^@ , y = sqrt2 sin315^@`

Note : `cos315^@ = cos45^@`

and `sin315^@ = -sin45^@`

The 'exact value of `cos45^@= 1/sqrt2`
The 'exact value' of `sin45^@ = 1/sqrt2`

`rArr x = sqrt2 cos45^@ = sqrt2 xx 1/sqrt2 = 1`

and y `=sqrt2(-sin45^@) = sqrt 2 xx -(1/sqrt2) = - 1`

`rArr (sqrt2 , 315^@ ) = ( 1 , - 1 )`