I really need your help to convert this $x^2+y^2+z^2=49$ to spherical coordinates.
I tried it and I got $(R\sin\phi\cos\theta)^2+(R\sin\phi\sin\theta)^2+(R\cos\phi)^2=49$.
But it says that it is wrong, or I have to simplify it. And I don't know if I am on the right track or not.
Any help will be appreciated, thanks.
This is equation of a sphere, so you can write immediately that $$R^2=49,$$ since $x^2+y^2+z^2=R^2$.
But you could get to this the way you started, simply by repeatedly using $\cos^2x+\sin^2x=1$ to simplify your final expression.
$$(R\sin\phi\cos\theta)^2+(R\sin\phi\sin\theta)^2+(R\cos\phi)^2= R^2\sin^2\phi(\cos^2\theta+\sin^2\theta)+R^2\cos^2\phi = R^2\sin^2\phi+R^2\cos^2\phi = R^2(\sin^2\phi+\cos^2\phi)= R^2$$