What is the Cartesian form of #(1,(-pi )/4)#?

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Answer 1 · 2017-07-21T13:48:50

#(1/sqrt2, -1/sqrt2)#

We're asked to find the Cartesian (rectangular) form of a polar coordinate.

We can use two simple equations to get the #x#- and #y#-coordinates:

#x = rcostheta#

#y = rsintheta#

Here.

So we have

#x = (1)cos(-pi/4) = color(red)(1/sqrt2#

#y = (1)sin(-pi/4) = color(blue)(-1/sqrt2#

The Cartesian form is thus

#(color(red)(1/sqrt2), color(blue)(-1/sqrt2))#