Sin^-1(x)
1/sqrt(1-x^2)
The notation sin^-1(x) represents the inverse sine function. The inverse sine function is a function that undoes the sine function. Specifically, the inverse sine function maps values between -1 and 1 to angles between -π/2 and π/2 (or between -90 degrees and 90 degrees).
Here’s an example of how to use the inverse sine function:
If we want to find the angle θ such that sin(θ) = 0.5, we can use the inverse sine function as follows:
sin^-1(0.5) = 30 degrees (or π/6 radians)
This tells us that the angle whose sine is 0.5 is 30 degrees (or π/6 radians).
Note that the inverse sine function is generally denoted as arcsin(x) instead of sin^-1(x) in many textbooks and calculators.
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