# inverse trigonometric functions

The inverse trigonometric functions are , and . These functions perform the reverse operations to the original trigonometric functions , and respectively. Recall that a function is invertible if it is one-to-one. Click here to revise inverse functions. Hence, before we can sketch the graphs of the inverse trigonometric functions, we must choose a domain for them for which they are one-to-one. Note that the original trigonometric functions work on angles and so each of the inverse trigonometric functions will return an angle. We use radians for all angles in the following – see more on radians. Also note that we use instead of , for example, as this can be confused with , the reciprocal trigonometric function.Â

## Inverse Trigonometric Function: arcsin(x)

Since is periodic, there are infinitely many regions for which it is one-to-one. We choose the default domain to be . The range of is . It follows that the domain of is and the range is . The graphs of and are reflections of one another in the line .

## Inverse Trigonometric Function: arccos(x)

Since is periodic, there are infinitely many regions for which it is one-to-one. We choose the default domain to be . The range of is . It follows that the domain of is and the range is . The graphs of and are reflections of one another in the line .

## Inverse Trigonometric Function: arctan(x)

Since is periodic, there are infinitely many regions for which it is one-to-one. We choose the default domain to be . The range of is all of . It follows that the domain of is and the range is . The graphs of and are reflections of one another in the line .