Question #288857

Express the following surfaces in spherical coordinates:


y² +z² -x² = 1


1
Expert's answer
2022-01-24T02:27:31-0500

In shperical coordinates:


x=rcosϕsinθy=rsinϕsinθz=rcosθx = r\cos \phi \sin \theta\\ y = r\sin \phi \sin\theta\\ z = r\cos \theta

Substituting into the equation, obtain:

r2sin2ϕsin2θ+r2cos2θr2cos2ϕsin2θ=1r2sin2θ(sin2ϕcos2ϕ)+r2cos2θ=1r2cos2θr2sin2θcos2ϕ=1r^2\sin^2 \phi \sin^2\theta +r^2\cos^2\theta-r^2\cos^2 \phi \sin^2\theta=1\\ r^2\sin^2\theta(\sin^2 \phi -\cos^2 \phi )+r^2\cos^2\theta=1\\ r^2\cos^2\theta - r^2\sin^2\theta\cos2\phi=1

Answer. r2cos2θr2sin2θcos2ϕ=1r^2\cos^2\theta - r^2\sin^2\theta\cos2\phi=1.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS