Trigonometric Equations and their Solutions

An algebraic equation like $x^2-5x+6=0$ is satisfied by only finitely many values of $x$. A trigonometric equation is an equation that involves one or more trigonometric functions of an unknown angle, for example $\sin\theta=\dfrac{1}{2}$, $\tan\theta=2$, or $\cos3\theta=\cos5\theta$. Because every trigonometric function repeats itself after one full period, a trigonometric equation behaves very differently from an algebraic one: once you find one value of $\theta$ that satisfies it, infinitely many more values (obtained by adding multiples of the period) satisfy it too. This chapter first pins down solutions inside a single period (the principal solutions), then builds a formula that captures every solution at on …