y = [tex]sin^{-1}x[/tex] function is represented in the graph.
What is inverse sine function?
The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle.
According to the graph
Domain = [-1, 1]
Range = [-[tex]\frac{\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex]]
Restrict the domain of the sine-function y =sinx, so that it is one to one, and not infinite by setting an interval [-[tex]\frac{\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex]].
The restricted function passes the horizontal line test, therefore it is one to one .
Each range value (-1 to 1) is within the limited domain (-[tex]\frac{\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex]).
Inverse sine function:
Inverse sine or arcsine is the inverse of the restricted sine function , y =sinx, [-[tex]\frac{\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex]].
The equation is y = [tex]sin^{-1}x[/tex] or y = arc sinx
Which also means , siny = x, where -[tex]\frac{\pi }{2}[/tex] ≤ y ≤ [tex]\frac{\pi }{2}[/tex], -1 ≤ x ≤ 1.
The coordinates of the inverse sine function (-1, -[tex]\frac{\pi }{2}[/tex]), (0, 0), (1, [tex]\frac{\pi }{2}[/tex]).
Thus, y = [tex]sin^{-1}x[/tex] function is represented in the graph.
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