Recall that we can apply trig functions to any angle , including large and negative angles. But when we consider the inverse function we run into a problem, because there are an infinite number of angles that have the same sine. For more on this see Inverse trigonometric functions. To solve this problem, the range of inverse trig functions are limited in such a way that the inverse functions are one-to-one, that is, there is only one result for each input value.
Range and domain of arcsin Recall that the domain of a function is the set of allowable inputs to it. The range is the set of possible outputs. So if you use a calculator to solve say arcsin 0. Home Contact About Subject Index. The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number. The symbol sin -1 is used often when one wishes more than one or even all the values possible even though these values are not covered by the Arcsine function.
See below for a better understanding of this. A function can only be an inverse if it is 1-to-1 and undoes exactly the desired function. See inverse function notes for a review of inverse functions. In the graph at the left, notice that the sine function, pink and dashed, is not 1-to-1 because it is periodic and repeats every 2.
The arcsine of zero is zero, sin -1 0 is 0. The arccosine of a negative number is a second quadrant angle, cos -1 - is in quadrant II. The arctangent of zero is zero, tan -1 0 is 0.
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