The discussion revolves around determining the domain of the function sin(arcsin(x)). Participants are exploring the relationship between the arcsine function and the sine function, particularly focusing on the implications of their domains and ranges.
The discussion is active, with participants offering insights into the properties of sine and arcsine. There is recognition of the need to clarify the domains and ranges involved, but no consensus has been reached regarding the interpretation of these functions.
Some participants note the importance of understanding the restrictions on the sine function to establish the relationship with arcsine. There is mention of the range of arcsin being [-1, 1] and the implications of this for the overall discussion.
HallsofIvy said:Since sine has all real numbers as domain, the domain of this function is the domain of arcsine. Do you understand why its domain is [-1, 1]?
The sine function is not a one-to-one function, so technically, there is no function which is the inverse of sine function.11thHeaven said:I understand why the domain of arcsin is [1,-1]. But if sine is the inverse of arcsine, shouldn't the domain of sine be the range of arcsine? I thought that was the rule where inverse functions are concerned.