How do you convert the polar coordinate (-2,5pi/4) into cartesian coordinates?

2 Answers
Alan P.
Oct 21, 2015

#(-2,(5pi)/4)# [polar] #= (sqrt(2), sqrt(2))# [Cartesian]

Explanation:

In Polar form:
#(-2,(5pi)/4) = (2,pi/4)#
(draw a diagram if this isn't obvious)

For an angle of #pi/4# the "opposite" and "adjacent" sides (i.e. #x# and #y#) are equal
and since #sqrt(x^2+y^2) = # the radius # = 2#

#rarr x=y = sqrt(2)#

Daniel L.
Oct 21, 2015

The solution is #(-sqrt(2);-sqrt(2))#. See explanation for details.

Explanation:

The given coordinates are not correct, because #r# cannot be negative (it is a distance between 2 points and it is either zero or a positive real number).

If the given point was #(2;(5pi)/4)# then corresponding Carthesian coordinates would be:

#x=rcosvarphi=2*cos((5pi)/4)=2*(-cos(pi/4))#

#=2*(-sqrt(2)/2)=-sqrt(2)#

#y=rsinvarphi=2*sin((5pi)/4)=2*(-sin(pi/4))#

#=2*(-sqrt(2)/2)=-sqrt(2)#

So the Carthesian coordinates are #(-sqrt(2);-sqrt(2))#

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