Chapter 1 | Functions and Graphs
87
(1.12) sin −1 ( x ) = y if and only if sin( y ) = x and − π 2 ≤ 2 ; cos −1 ( x ) = y if and only if cos( y ) = x and0≤ y ≤ π . The inverse tangent function, denoted tan −1 or arctan, and inverse cotangent function, denoted cot −1 or arccot, are defined on the domain D ={ x | −∞< x <∞} as follows: (1.13) tan −1 ( x ) = y if and only if tan( y ) = x and − π 2 < y < π 2 ; cot −1 ( x ) = y if and only if cot( y ) = x and0< y < π . The inverse cosecant function, denoted csc −1 or arccsc, and inverse secant function, denoted sec −1 or arcsec, are defined on the domain D ={ x | | x | ≥1} as follows: (1.14) csc −1 ( x ) = y if and only if csc( y ) = x and − π 2 ≤ y ≤ π 2 , y ≠0; sec −1 ( x ) = y if and only if sec( y ) = x and0≤ y ≤ π , y ≠ π /2. y ≤ π
To graph the inverse trigonometric functions, we use the graphs of the trigonometric functions restricted to the domains defined earlier and reflect the graphs about the line y = x ( Figure 1.41 ).
Figure 1.41 The graph of each of the inverse trigonometric functions is a reflection about the line y = x of the corresponding restricted trigonometric function.
Go to the following site (http://www.openstax.org/l/20_inversefun) for more comparisons of functions and their inverses.
Made with FlippingBook - professional solution for displaying marketing and sales documents online