Guest said:What's $\arcsin(\sin(\frac{−3\pi}{2}))?$ I think it's equal to
$\arcsin(-\sin(\frac{3\pi}{2})) =\arcsin(-\sin(\pi+\frac{\pi}{2})) = \arcsin(\sin(\pi/2)) = \frac{\pi}{2}$
Is this correct?
The value of $\arcsin(-\sin(\frac{3\pi}{2}))$ is undefined. This is because the range of the inverse sine function is limited to $[-\frac{\pi}{2}, \frac{\pi}{2}]$, and $\frac{3\pi}{2}$ falls outside of this range.
The value is undefined because the inverse sine function is not defined for values outside of its range. This is due to the fact that there are multiple angles that have the same sine value, so it is not possible to uniquely determine the angle.
No, there are no restrictions that can be placed on the input to make the value defined. This is because the sine function is periodic, so any multiple of $2\pi$ will also result in an undefined value for the inverse sine function.
The domain of the function $\arcsin(-\sin(x))$ is the set of all real numbers.
No, it is not possible to approximate the value of $\arcsin(-\sin(\frac{3\pi}{2}))$ because it is undefined. However, we can approximate the value of $\sin(\frac{3\pi}{2})$ to be -1, which is the value of the inner sine function. But this does not give us any information about the inverse sine function.