No, it isn't. The graphs of the two functions are close together when x is in the interval [-.5, .5], but they aren't identical.esha said:the graph of sin inverse (sin x) between the domain of ( -pi/2,pi/2) is y = x.
What expression? Are you trying to understand why the graph of ##y = \sin^{-1}(x)## looks the way it looks? Are you asking how the values on this graph are calculated? If you have studied calculus, one of the topics presented later is infinite series. One such series is the expansion for the arcsine function. See https://math.stackexchange.com/questions/197874/maclaurin-expansion-of-arcsin-x.esha said:but after it crosses that domain of course the expression won't be the same anymore because sin inverse has its principle value as ( - pi/2, pi/2) due to sin x many to one natured function. now the way these expressions change is what doesn't seem intuitive to me. can anybody please tell me how to derive those expressions logically?
It wasn't clear to me what you were asking about, which is the graph of ##y = \sin^{-1}(\sin(x))##. On the interval ##[-\pi/2, \pi/2]##, the graph of this function is the same as that of y = x, which is what you said.esha said:its not sin inverse graph..
that's pretty straight forward..
. m talking bout sin inverse ( sin x) graph
The domain of the graph of sin inverse (sin x) after the domain of (- pi/2, pi/2) is the interval [0, pi]. The range is the interval [-pi/2, pi/2]. This means that the graph only exists between 0 and pi on the x-axis, and between -pi/2 and pi/2 on the y-axis.
The shape of the graph of sin inverse (sin x) after the domain of (- pi/2, pi/2) is a series of straight lines connected at the endpoints. This is because the inverse of sin x is a piecewise function, meaning it has different rules for different intervals on the x-axis.
The graph of sin x is a smooth, continuous curve, while the graph of sin inverse (sin x) after the domain of (- pi/2, pi/2) is a series of straight lines. Also, the domain and range of the two graphs are different, as the graph of sin x extends to infinity in both directions on the x-axis, while the graph of sin inverse (sin x) is limited to the interval [0, pi].
The period of the graph of sin inverse (sin x) after the domain of (- pi/2, pi/2) is pi. This means that the graph repeats itself every pi units on the x-axis.
The graph of sin inverse (sin x) after the domain of (- pi/2, pi/2) represents the angle measure of an angle on the unit circle. The x-value of a point on the graph corresponds to the angle measure in radians, while the y-value corresponds to the sine of that angle. This is similar to how the unit circle is used to find the sine of an angle in trigonometry.