I was asked to convert $x^2-y^2-z^2=1$ to spherical coordinate equation.
What I do is substitute $x = \rho \sin(\varphi)\cos(\theta)$, $y = \rho \sin(\varphi)\sin(\theta)$ and $z = \rho \cos(\varphi)$ to get the equation: $$(\rho \sin(\varphi)\cos(\theta))^2 - (\rho \sin(\varphi)\sin(\theta))^2 - (\rho \cos(\varphi))^2=1$$ Then I simplify it into: $$\rho^2 \sin^2(\varphi) \cos(2\theta) - \rho^2\cos^2(\varphi) = 1$$ But when I submit it in Webassign, they still mark it wrong. I only have 1 submit left so I am very apprecitated if someone point out what I did wrong. Thank you!