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Explore the definitions and differentiation of inverse trigonometric functions and antiderivative formulas involving them. Learn about arcsine, arccosine, arctangent, arcsecant, and more.
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Section 7.6 Inverse Trigonometric Functions
THE INVERSE SINE FUNCTION Definition: The inverse sine or arcsine function. For −1 ≤ x ≤ 1,
THE INVERSE COSINE FUNCTION Definition: The inverse cosine or arccosine function. For −1 ≤ x ≤ 1,
THE INVERSE TANGENT FUNCTION Definition: The inverse tangent or tangent function. For all real x,
THE INVERSE SECANT FUNCTION Definition: The inverse secant or arcsecant function. For | x | ≥ 1,
The definitions for inverse cosecant and inverse cotangent are on page 458 of the text. The derivatives of inverse cosecant and inverse cotangent are also on page 459 of the text.
GENERALIZED ANTIDERIVATIVE FORMULAS INVOLVING INVERSE TRIG. FUNCTIONS