What is the range of the function \(y=\log_2 (\sqrt{\cos x})\) for \(-90^\circ< x < 90^\circ\)?
+128408 We only really need to look at 0 ≤ x < 90
When x = 0
cos 0 = 1 sqrt ( cos 0) = sqrt (1) = 1
So y = log2 1 = 0
When x is almost 90
cos (almost 90) = almost 0 = a very small positive
So
log 2 sqrt (a very small positive) = log 2 (a very small positive) = a very large negative
So...as the guest found, the range is (-inf, 0 ]
