Inverse Trigonometric Functions

Step 1: Understanding the principal value of $%5Csin%5E%7B-1%7D$ .
The principal value of $%5Csin%5E%7B-1%7D%20x$ is the value of the angle $%5Ctheta$ such that $%5Csin%20%5Ctheta%20%3D%20x$ and $%5Ctheta%20%5Cin%20%5Cleft%5B%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5Cright%5D$ .

Step 2: Applying the value.
We are given $%5Csin%5E%7B-1%7D%20%5Cleft(%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%5Cright)$ , which corresponds to the angle $%5Ctheta%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D$ because $%5Csin%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D$ .

Step 3: Conclusion.
Thus, the principal value of $%5Csin%5E%7B-1%7D%20%5Cleft(%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%5Cright)$ is $%5Cfrac%7B%5Cpi%7D%7B4%7D$ .

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Inverse Trigonometric Functions

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs