Density in the unit sphere Prove that $\left\{ ( \sin a \cos b , \cos a\cos b , \sin b)\mid a , b \in \mathbb{N} \right\}$ is dense in the unit sphere.

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Because $\cos(n)$ and $\sin(n)$ (for n an integer) are dense on the interval $[0,1]$ (because $\pi$ is irrational) and those map continu to your coordinates.
Because $\cos(n)$ and $\sin(n)$ (for n an integer) are dense on the interval $[0,1]$ (because $\pi$ is irrational) and those map continu to your coordinates.