Inverse Functions

Inverse Sine Function

Range:

On this interval, y=arcsin x.

Evaluating the Inverse Sine Function

                                    

For this problem we would find an angle whose sine is equal to -1/2.





on the interval 




So we get:

Inverse Cosine Function

                                    Range: 

On this interval, y=arccos x. 

For this problem, we need to find an angle whose cosine equals: 

,  so

Inverse Properties

sin(arcsin x )= x  and arcsin(siny) = y when

   and

cos(arccos x) = x and arccos(cosy) = y when 

and 

tan(arctan x) = x and arctan(tan y) = y  when

x is a real number and 

-5 lies on the domain of arctan x, so we can use the inverse property, and we get: