if sin0 = 1/6 and π/2 < 0 < π, find cos0.
Since sin 0 = 1/6, we can use the Pythagorean identity sin^2(0) + cos^2(0) = 1 to find cos 0.
First, we need to find sin^2(0). We know that sin^2(0) + cos^2(0) = 1, so rearranging the equation gives cos^2(0) = 1 - sin^2(0).
Plugging in sin^2(0) = (1/6)^2 = 1/36, we have cos^2(0) = 1 - 1/36 = 35/36.
Taking the square root of both sides, we get cos(0) = ±√(35/36).
Note that since π/2 < 0 < π, we are in the second quadrant. In the second quadrant, cosine is negative. Therefore, cos(0) = -√(35/36).