‘Sines, cosines, and their relatives’ begins by defining the basic trigonometric functions—sine, cosine, and tangent—and explaining their use. These functions are geometric quantities defined using the ratios of the Opposite, Adjacent, and Hypotenuse sides of the right triangle. Less common functions are the cosecant, secant, and cotangent functions. The history of the naming of the trigonometric functions is discussed along with an explanation of even more obscure functions: the versed sine, versed cosine, exsecant, and excosecant. The versed sine was used frequently in practical applications like astronomy, navigation, and surveying. Finally, inverse trigonometric functions and graphs of trigonometric functions are considered.