Find the equation of the tangent plane of each of the following surface patches at the indicated points.
Compute $\sigma_r \times \sigma_\theta = (-2r\cosh\theta, 2r^2 \sinh \theta, r)$. Since $\sigma(1,0) = (1,0,1)$, the vector $\sigma_r \times \sigma_\theta(1,0) = (-2,0,1)$ is normal to the tangent plane at $(1,0,1)$. The equation of the plane is $(-2,0,1) \cdot (x - 1, y - 0, z - 1) = 0$, or $2x - z = 1$.