The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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Inverse trigonometric functions are the inverse of the different trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant. The inverse of a function is simply the reflection of that function about the line x = y and for inverse trigonometric functions is expressed as f-1(x). The inverse trigonometric functions are expressed as sin-1x (or arcsin x), cos-1x (or arccos x), tan-1x (or arctan x), cot-1x (or arccot x), sec-1x (or arcsec x), and csc-1x (or arccsc x). The trigonometric functions are based on complex exponentials and so the inverse of such functions can be expressed in terms of the natural logarithmic function, ln. Although this is true it is much more practically useful to define the inverse functions in terms of side measurements of triangles as they relate to the angles in the triangle when solving geometric problems.
Inverse trigonometric functions are periodic since they are derived from trigonometric functions that are circular in nature. Since they are not one to one functions the domain must be restricted for each inverse trigonometric function just as in the case of the trigonometric functions. The restricted domains for each function are as follows:
The inverse trigonometric functions are examples of transcendental functions. Although these inverse functions are usually employed in problems that require finding angles from side measurements in triangles, when they are written in terms of natural logarithmic functions they are also useful as antiderivatives for a wide variety of functions. In this sense they are often utilized in solving differential equations that arise in mathematics, engineering and physics.