7 - More on Trigonometric Functions and the Hyperbolic Functions

Abstract

This chapter discusses the trigonometric functions and the hyperbolic functions. The inverse sine function is the function that assigns to each number x in [−1, 1] the unique number y in [−π/2, π/2] such that x = sin y. Thus, one can write, y = sin-1x. However, the −1 appearing in equation does not mean l/(sin x), which is equal to (sin x)-1 =cos x. Another commonly used notation for the inverse sine function is y = arcsine x. The inverse cosine function is the function that assigns to each number x in [−1, 1], the unique number y in [0, π] such that x =cos y. Thus, one can write, y =cos-1x, and cos-1x is also written as arccos x. The inverse hyperbolic sine function, on the other hand, is defined by y = cos-1x if and only if x =sinhy. The domain of y = sin-1x is (−∞, ∞).