In this section, we will introduce the inverse trigonometric functions and construct their derivative formulas.

A function is called one-to-one if whenever it must be true that. That is, an output value cannot come from two different input values.

A function is called one-to-one if whenever it must be true that. That is, an output value cannot come from two different input values. This function is not one-to-one.

A function is called one-to-one if whenever it must be true that. That is, an output value cannot come from two different input values. Significance: Only one-to-one functions have inverse functions.

Below is shown the graph of This function is not one-to-one and so has no inverse function.

Below is shown the graph of This function has an inverse. Consider restricting the domain of the sine function to: This is the function in blue shown to the left.

The function is the inverse of the sine function with restricted domain. That is, the arcsin(x) is the angle θ in the interval with.

Below is shown the graph of This function is not one-to-one and so has no inverse function.

Below is shown the graph of This function has an inverse. Consider restricting the domain of the cosine function to: This is the function in blue shown to the left.

The function is the inverse of the cosine function with restricted domain. That is, the arccos(x) is the angle θ in the interval with.

Below is shown the graph of This function is not one-to-one and so has no inverse function.

Below is shown the graph of This function has an inverse function. Consider restricting the domain of the tangent function to: This is the function in blue shown to the left.

The function is the inverse of the tangent function with restricted domain. That is, the arctan(x) is the angle θ in the interval with.

Use the definitions of the section to find the exact value of.

Use the definitions of the section to find the exact value of.

Use the definitions of the section to find the exact value of.

Use the definitions of the section to find the exact value of.

The following are true:

Find the derivative of the function.