Power functions and first sketches practice question 12

Only one part of $T(t)$ changes with $t$. When is that part as large as it can be?

The constant $36.9$ and the positive amplitude $0.4$ do not move the peak. $T$ is largest when the sine equals $1$, which happens when its input is $\tfrac{\pi}{2}$ plus a whole number of turns.

Solve $\tfrac{\pi}{12}(t - 11) = \tfrac{\pi}{2}$, and check that your $t$ lies between $0$ and $24$.