Sin^-1(√2/2)
π/4
The inverse sine function, denoted as sin^-1 or arcsin, is the inverse operation of the sine function. It is defined as the angle whose sine is equal to a given number, within a certain range.
To find sin^-1(√2/2), we need to determine the angle whose sine is √2/2. We know that the sine function is positive in the first and second quadrants, and that it has a maximum value of 1 at 90° and a minimum value of -1 at -90°. Since sin(45°) = √2/2, we can conclude that:
sin^-1(√2/2) = 45° + 360°k or 180° – 45° + 360°k
where k is an integer that represents the number of full rotations around the unit circle.
Therefore, sin^-1(√2/2) = 45° or 135°, depending on the context. We could also represent it in radians as π/4 or 3π/4, respectively.
In summary, sin^-1(√2/2) has two possible values, and the choice of which one to use depends on the context and the range of angles that we are considering.
More Answers:
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