Inverse Of A Function

Step 1: Evaluate each term

%5Ctan%5E%7B-1%7D(1)%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%2C%20%5Cquad%20%5Ccos%5E%7B-1%7D%5Cleft(-%5Cfrac%7B1%7D%7B2%7D%5Cright)%20%3D%20%5Cpi%20-%20%5Cfrac%7B%5Cpi%7D%7B3%7D%2C%20%5Cquad%20%5Csin%5E%7B-1%7D%5Cleft(-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Cright)%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B4%7D.

Step 2: Add the terms

%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2B%20%5Cleft(%5Cpi%20-%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright)%20-%20%5Cfrac%7B%5Cpi%7D%7B4%7D.

Simplify:

%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20-%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B3%7D.

Conclusion: The principal value is

%5Cfrac%7B2%5Cpi%7D%7B3%7D

Chapter Questions
1 MCQs