if sin0 = 1/6 and π/2 < 0 < π, find cos0.
cos0 = ?
Since sin0 = 1/6 and π/2 < 0 < π, we know that the value of 0 lies in the second quadrant. In the second quadrant, the value of cos0 is negative.
To find cos0, we can use the Pythagorean identity: sin^2(0) + cos^2(0) = 1
Substituting sin0 = 1/6, we have:
(1/6)^2 + cos^2(0) = 1
1/36 + cos^2(0) = 1
cos^2(0) = 1 - 1/36
cos^2(0) = 35/36
Taking the square root of both sides, we find:
cos0 = ±√(35/36)
Since cos0 is negative in the second quadrant, we have:
cos0 = -√(35/36)
So, cos0 = -√35/6