Geometric Interpretation of cylindrical and spherical coordinates

Question

Im just wondering how I would go about geometrically interpreting these equations.

$$\rho \sin\phi = 1 $$ $$\cos \phi = \frac{-\sqrt2}{2}$$ $$\rho \cos \phi = 1$$

Answer 1

HINT

In spherical coordinates indicating with $\phi$ the angle between $OP$ and $z$ axis we have that

• $\rho \sin\phi$ is the length of the projection of $OP$ onto $x-y$ plane
• $\cos \phi = k$ is a fixed value for $\phi$
• $\rho \cos \phi=z$