Basic Technical Mathematics, 11th Edition

20.6 The Inverse Trigonometric Functions

• Inverse Functions • Inverse Trigonometric Functions • Ranges of the Inverse Trig Functions

When we studied the exponential and logarithmic functions, we often changed an expression from one form to the other. The exponential function $y\hspace{0.17em}=\hspace{0.17em}{b}^x\hspace{0.17em},\hspace{0.17em}$ written in logarithmic form with x as a function of y, is $x\hspace{0.17em}=\hspace{0.17em}{\log }_{b}y\hspace{0.17em}.\hspace{0.17em}$ Then we wrote the logarithmic function as $y\hspace{0.17em}=\hspace{0.17em}{\log }_{b}x\hspace{0.17em},\hspace{0.17em}$ because it is standard practice to use y as the dependent variable and x as the independent variable.

These two functions, the exponential function $y\hspace{0.17em}=\hspace{0.17em}{b}^x$ and the logarithmic function $y\hspace{0.17em}=\hspace{0.17em}{\log }_{b}x\hspace{0.17em},\hspace{0.17em}$ are called inverse functions (see page 379). This means that if we solve for the independent variable in terms of the dependent variable ...