Inverse Trig Functions - Cornell University

Inverse Trig Functionsc A Math Support Center CapsuleFebruary 12, 2009 IntroductionJust as trig Functions arise in many applications, so do the Inverse trig Functions . Whatmay be most surprising is that they are useful not only in the calculation of angles giventhe lengths of the sides of a right triangle, but they also give us solutions to some commonintegrals. For example, suppose you need to evaluate the following integral: ba1 1 x2dxfor some appropriate values ofaandb. You can use the Inverse sine function to solveit! In this capsule we do not attempt to derive the formulas that we will use; you shouldlook at your textbook for derivations and complete explanations.

Definitions of the Inverse Functions When the trig functions are restricted to the domains above they become one-to-one func-tions, so we can define the inverse functions. For the sine function we use the notation sin−1(x) or arcsin(x). Both are read “arc sine” . Look carefully at where we have placed the -1.

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