Find the exact value of inverse sine of sine of a third 𝜋 in radians.
There are two ways to solve this problem. The first is to evaluate sine of a third 𝜋 then find the inverse sine of that number. However, by considering what the inverse really means, we should be able to save ourselves a little bit of time.
Remember the inverse is the opposite of a function. The inverse of multiplying is dividing. The inverse of adding is subtracting. And the inverse of the sine function is inverse sine.
For any trigonometric functions, therefore, the inverse function of the function in terms of 𝜃 is just 𝜃. In this case then, the inverse sine of sine of a third 𝜋 is simply a third 𝜋.