How to Graph Inverse Trigonometric Functions?

Inverse trigonometric functions are also called arc functions. Just like trigonometric functions, we can also display diagrams of inverse trigonometric functions.

Related Topics

• How to Evaluate Trigonometric Function?
• How to Solve Angles and Angle Measure?
• How to Solve Coterminal Angles and Reference Angles?

Step-by-step guide to inverse trigonometric functions graph

We can plot diagrams of different inverse trigonometric functions with their range of principal values. Here, we select the random values for \(x\) in the domain of the corresponding inverse trigonometric functions.

Arcsine function

The Arcsine function, or inverse sine function, also known as \(sin^{-1}x\), is the inverse of the sine function. The diagram of the sine inverse function is as follows:

Arccosine function

The Arccosine function, or inverse cosine function, also known as \(cos^{-1} x\), is the inverse of the cosine function. The diagram of the cos inverse function is as follows.

Arctangent function

The Arctangent function, or inverse tangent function, also display by \(tan^{-1} x\), is the inverse of the tan function. The graph of the tan inverse function is as follows.

Arccotangent function

The Arccotangent function or inverse cotangent function, also shown as \(cot^{-1} x\), is an inverse of the cotangent function. The graph of the cot inverse function is as follows.

Arcsecant function

The Arcscant function, or inverse sequence function, also denoted by \(sec^{-1} x\), is the inverse of the secant function. The diagram of the inverse sec function is as follows.

Arccosecant function

The Arccosecant function, or inverse cosecant function, also known as \(cosec^{-1} x\), is the inverse of the cosecant function. The inverse function diagram of cosec is as follows.

Inverse trigonometric functions domain and range

The charts above help us compare and understand the functions \(y=sin^{-1}x\), \(y=cos^{-1}x\), \(y=tan^{-1}x\), \(y=cot^{-1}x\), \(y=sec^{-1}x\), \(y=cosec^{-1}x\). The domain(\(x\) value) of the function is presented along the \(x\)-axis and the range(\(y\) value) of the inverse trigonometric function is presented along the \(y\)-axis. The table below shows the domain and range of the principal values of the inverse trigonometric functions.