In the preceding chapters, you have defined and applied the six basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. The input for each of these functions is an angle (typically measured in radians or degrees) and the output is a real number value. For example, cos (π/3) = 1/2. This chapter explores the inverse trigonometric functions, which reverse the domain and range of the original functions. The inverse of cos x is arccos x, so arccos (1/2) = π/3.
A function is a set of inputs and outputs with one condition: Every input is paired with only one output. If you go one step further and guarantee that every output of a function is matched to only one input, then the function is called “one-to-one.”
Why does it matter? Only one-to-one functions have inverses, and that’s a problem when you deal with periodic functions, including all of the trig functions. Enough spoilers. Time to get started.