Trigonometric equations

A trigonometric equation is an equation in which the unknown appears as the argument of one or more trigonometric functions ($\sin$, $\cos$, $\tan$, $\cot$). Solving it means finding all the values of the angle $x$ that satisfy it: because of the periodicity of the trigonometric functions these values are infinitely many and are expressed in the form $x = x_0 + k\cdot T$, where $T$ is the period and $k\in\mathbb{Z}$.

In this chapter we distinguish four large families of trigonometric equations, each with its own solution method: elementary equations, equations solvable by substitution, linear equations in $\sin$ and $\cos$ and finally second-degree homogeneous equations (or ones reducible to them).

Sections

• Elementary equations
• Equations solvable by substitution
• Linear equations in sine and cosine
• Second-degree homogeneous equations

Exercises

• All the worked exercises of the chapter