Part 4/6:
- The inverse cosine function is thus defined as ( y = \arccos(x) ), taking input values from -1 to 1 as well, but outputting angles from 0 to ( \pi ).
The arcsine and arccosine functions intercept at certain key points, and they reflect over the appropriate axes just like the arcsine does.
The Tangent Function
For the tangent function, ( y = \tan(x) ):
This function also has multiple outputs for a single input, and its asymptotes complicate things further. Thus, it is conventionally restricted to the interval ( (-\frac{\pi}{2}, \frac{\pi}{2}) ) for its inverse.
The inverse, ( y = \arctan(x) ), varies from ( -\infty ) to ( +\infty ) but is confined in its angle values from ( -\frac{\pi}{2} ) to ( \frac{\pi}{2} ).