Sinusoidal syndrome

A person whose happiness if measured on a happy o' meter would behave sinusoidally (the graph would look like a sine wave).

If Fred's happiness varies sinusoidally because he has sinusoidal syndrome and he is completely sad (0) at time 5.2 and goes to completely happy (10) at time 12.8 what is the trigonometric function for his mood?

The math teacher went off on another tangent and began rambling about people whose moods vary sinusoidally because of their having sinusoidal syndrome.

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