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

1 Answer
Jan 21, 2016

Answer:

( 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 )#