# Going from Spherical coordinates to Cartesian

1. Homework Statement

Convert the point (rho,theta,phi) = (6, (5pi)/4, pi/2) to Cartesian coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place.

3. The Attempt at a Solution

{x}=r*sintheta*cosphi
{y}=r*sintheta*sinphi
{z}=r*costheta

So

x = 6*sin(5pi/4)*cos(pi/2)
y = 6*sin(5pi/4)*sin(pi/2)
z = 6*cos(5pi/4)

x = 0
y = -4.242640687 (+2pi)
z = -4.242640687 (+2pi)

What did I do wrong?

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Dick
Homework Helper
Don't know. It looks reasonable so far. But you should be warned that mathematicians and physicists use different convention for the meaning of the angles in spherical coordinates. Are you sure you got the coordinate change from the same source as the problem? But I'm not sure what the (+2pi) is supposed to mean.

Because my answer is negative, don't I add 2pi to get the correct positive answer, as is the law of angles in this format?

[(-4.24264068712,-4.24264068712,3.67381906147E-16)]

Dick
Homework Helper
Because my answer is negative, don't I add 2pi to get the correct positive answer, as is the law of angles in this format?

[(-4.24264068712,-4.24264068712,3.67381906147E-16)]
Your answer is {x,y,z}. Those aren't angles. You can't add anything to them. Where did you get that 'answer'? I'm guessing because of the E-16 from some kind a 'calculator device'. Are you sure that is using the same conventions as the problem source?

Yeah, it's an online homework system. WAMAP.

Dick
Homework Helper
Oh, great. I don't know what WAMAP means either. But from the -4.24264068712 and E-16 which should in any reasonable universe be written as '0', you weren't completely off.

HallsofIvy
The reason I ask is that engineers swap "$\theta$" and "$\phi$" from what mathematicians use. Is $\phi$ the "co-latitude" and $\theta$ the "longitude" or vice-versa?