Question

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

Answer 1

`(-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)`

Answer 2

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))`