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))

Related questions
See all questions in Converting Coordinates from Polar to Rectangular
Impact of this question
12760 views around the world
You can reuse this answer
Creative Commons License