Understanding the Arcsin Function | Definition, Notation, and Domain

sin^(-1)x or arcsin(x)

Sin^(-1)x, or arcsin(x), is the inverse function of the sine function

Sin^(-1)x, or arcsin(x), is the inverse function of the sine function. It is a mathematical function that takes as input a value between -1 and 1 and returns an angle, measured in radians, whose sine is the input value. In other words, if y = sin^(-1)x, then sin(y) = x.

The notation “sin^(-1)x” can be a bit confusing, as it may seem to imply raising the sine function to the power of -1. However, in this case, the superscript -1 does not represent the reciprocal or multiplicative inverse. Instead, it denotes the inverse function.

The arcsin function is commonly used to find the angle (in radians) whose sine matches a given value. For example, if we want to find the angle whose sine is 0.5, we can express it as arcsin(0.5), which is approximately equal to 0.5236 radians or about 30 degrees.

It’s important to note that the arcsin function has a restricted domain of -1 to 1, since the sine function only takes on values in that range. If you try to evaluate arcsin(x) for a value of x outside this range, it will result in an error.

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