Section 5.5 Inverse Trigonometric and Hyperbolic Functions - Maple Application Center
Application Center Applications Section 5.5 Inverse Trigonometric and Hyperbolic Functions

## Section 5.5 Inverse Trigonometric and Hyperbolic Functions

Authors
: Dr. John Mathews
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We expressed the trigonometric and hyperbolic functions in Section 5.4 in terms of the exponential function. In this section we look at their inverses. When we solve equations such as w = sin(z); for z;, we will obtain formulas that involve the logarithm. Since trigonometric and hyperbolic functions are all periodic, they are many-to-one, hence their inverses are necessarily multivalued. The formulas for the inverse trigonometric functions are given by arcsin(z) = -i*log(i*z+sqrt(1-z^2));, arccos(z) = -i*log(z+i*sqrt(1-z^2));, and arctan(z) = i/2; log((i+z)/(i-z));.

#### Application Details

Publish Date: October 01, 2003
Created In: Maple V
Language: English

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