Find the exact value sin^-1(square root 2/2)
We know that sin^-1(y) is the angle whose sine is y. In this case, we are looking for the angle whose sine is (√2)/2.
Since the sine of an angle measures the length of the side opposite the angle divided by the length of the hypotenuse, we can imagine a right triangle where the side opposite the angle is (√2) and the hypotenuse is 2.
Using the Pythagorean theorem, we can find the other side of the triangle:
a^2 + b^2 = c^2
(√2)^2 + b^2 = 2^2
2 + b^2 = 4
b^2 = 2
b = √2
So, the other side of the triangle is √2.
Now we can find the angle whose sine is (√2)/2. Since sine is positive in the first and second quadrants, we are looking for an angle between 0 and 180 degrees.
Now, we know that sin(45°) = (√2)/2, so the angle we're looking for is 45 degrees.
Thus, the exact value of sin^-1((√2)/2) is 45 degrees.