How do you find the rectangular coordinates of the point whose spherical coordinates are #(4, 3π/4, π/3)#?

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Answer 1 · 2015-02-20T14:54:31

The answer is: #(sqrt2,sqrt6,-2sqrt2)#.

The formulas are:

#x=rsinthetacosphi#

#y=rsinthetasinphi#

#z=rcostheta#

So:

#x=4sin(3/4pi)cos(pi/3)=4*sqrt2/2*1/2=sqrt2#

#y=4sin(3/4pi)sin(pi/3)=4*sqrt2/2*sqrt3/2=sqrt6#

#z=4cos(3/4pi)=4*(-sqrt2/2)=-2sqrt2#.