Part 3/6:
Starting with the sine function, ( y = \sin(x) ):
Graphically, sine oscillates infinitely within the range of -1 to 1, making it not a one-to-one function.
To create its inverse, we restrict the domain of the sine function to ( [-\frac{\pi}{2}, \frac{\pi}{2}] ).
With this restriction, the inverse sine (arcsine) can be defined, leading to ( y = \arcsin(x) ) where ( x ) now takes values from -1 to 1.
When represented graphically, the arcsine function appears as a reflection of the sine function across the line ( y = x ). It represents angles for a given sine ratio.
Cosine and Its Inverse
Similarly for the cosine function, ( y = \cos(x) ):
- Again, the function is not one-to-one; hence we restrict it to the domain ( [0, \pi] ).