Let $f$ and $g$ be two trigonometric functions of the variable $x$. Solving the equation $f(x) = g(x)$ is determining the set $S$ of numbers $r$ for which $f(r) = g(r)$ is a true sentence. This set is the solution set (or truth set) of the equation. The story Trigonometric equations appeared long before they had that name: Greek, Indian and Arab astronomers needed to find the arc that has a given sine to convert observations into positions in the sky. The most famous of these is the Kepler equation, published in Astronomia nova (1609):