28: The domain is D( f ) = ℝ.
The second derivative is

Dividing points: The equation f ′′(x) = 0 is best solved by replacing cosine squared with 1 − sin²:

f ′′(x) = 4sin²(x) − 2sin(x) − 2

and then substituting y for sine. The resulting quadratic equation has roots y = 1 and y = −1/2, which yields dividing points x = π/2 + 2kπ, x = 7π/6 + 2kπ, x = 11π/6 + 2kπ.
There are no points in D( f ) where the second derivative does not exist.

The function is 2π-periodic, so you get to see concavity best if you draw the chart for, say, two neighboring periods.

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