Graph y = sinx and y = Arcsinx to show the difference between the two.Show complete solution and explain the answer.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember what the inverse of sine function is, hence `sin alpha = x =gt alpha = arcsin x` .

You should remember that the domain of the sine function represents the range of arcsine function and the range of sine function denotes the domain of arcsin function.

Hence, the domain of the sine function and the range of the arcsin function is the interval `[-pi/2 ; pi/2].` The range of sine function and the domain of arcsin function is the interval `[-1;1].`

The graph of the sine and arcsin functions are represented below such that, the black curve represents the graph of sin x and the red curve represents the graph of arcsin x:

Hence, you may sketch the graph of arcsin function (red curve) mirroring the graph of sine function (black curve) over the line y=x.

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