find the exact value of sin^-1 (-1/2)
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To find the exact value of sin^-1 (-1/2), we need to find the angle whose sine is -1/2.
We know that the sine function is equal to opposite/hypotenuse in a right triangle. So, in this case, we can consider a right triangle with an angle θ where sin(θ) = -1/2. In this scenario, the opposite side would be -1 and the hypotenuse would be 2.
Using the Pythagorean theorem, we can find the adjacent side:
a^2 + (-1)^2 = 2^2
a^2 + 1 = 4
a^2 = 3
a = √3
Now, we can set up the right triangle with opposite side -1, adjacent side √3, and hypotenuse 2.
The angle θ in this triangle is 30 degrees or π/6 radians. So sin^-1 (-1/2) = 30 degrees or π/6 radians.