arcsin(x)
1/√(1-x^2)
The function arcsin(x) represents the inverse sine function, which gives us the angle whose sine equals x. It is only defined for values of x in the range [-1, 1].
The function has a domain of [-1, 1], and a range of [-π/2, π/2]. The graph of arcsin(x) is a reflection of the part of the sine function graph that lies in the first and second quadrants, across the line y=x. It is a single-valued function, meaning that it gives a unique output for every input in its domain.
Some important properties of arcsin(x) include:
1. The derivative of arcsin(x) is 1/√(1-x²).
2. The integral of 1/√(1-x²) is arcsin(x) + C, where C is a constant.
It is important to note that the output of arcsin(x) is an angle measured in radians, not a numerical value. To convert this angle to degrees, you need to multiply by 180/π.
Also, since arcsin(x) only gives us one value for each input, it is important to be aware of the fact that it can only give us an angle in a certain quadrant. If you need to find all the possible angles whose sine equals x, you need to add or subtract multiples of 2π.
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