Question

Use complete sentences to explain why it is not possible to simplify the following trigonometric expression.

sin(arcsin(2))

Answer 1

This is not possible because arcsin is the angle that will give you a sine value of 2.  Sine values range from -1 to 1; there is no angle that will give you a sine of 2.

Answer 2

Arcsin(X) is the inverse function of the Sin function.

This means that Arcsin(X) gives you the value Y that you need to input in the function of Sin in order to have Sin(Y) = X

Here you can see that we have Arcsin(2), this would be equal to a number that when you put it inside the sin function, you have

Sin(Y) = 2, but as you know, the range of the sin function is from -1 to 1, so you never can have Sin(Y) = 2, this is why this expression can not be simplified.