Sin^-1(√2/2)
To find the value of inverse sine for √2/2, we need to use the trigonometric identity for the special right triangle in the unit circle
To find the value of inverse sine for √2/2, we need to use the trigonometric identity for the special right triangle in the unit circle.
In a unit circle, the sinθ is equal to the y-coordinate of the point on the circle corresponding to the angle θ. Since we have sin^-1(√2/2), we need to find the angle whose sine is √2/2.
For the given value, √2/2, if we draw a right triangle with a hypotenuse of length 1 (unit circle), the length of one of the legs will be √2/2.
Since the length of one leg is √2/2, it means that the lengths of both legs of the right triangle are equal, making it an isosceles right triangle. In an isosceles right triangle, the two angles other than the right angle are 45 degrees each.
Therefore, sin^-1(√2/2) is equal to 45 degrees or π/4 radians.
So, sin^-1(√2/2) = 45° or π/4 radians.
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