The maximum angle is 12 degrees, so the amplitude of the theta function is 12. As well, a complete cycle is 2 seconds. The period of a periodic trig function is `k={2pi}/T={2 pi}/2=pi` , where k is the scaling factor inside the sine function.

For a sine function, we have:

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The maximum angle is 12 degrees, so the amplitude of the theta function is 12. As well, a complete cycle is 2 seconds. The period of a periodic trig function is `k={2pi}/T={2 pi}/2=pi` , where k is the scaling factor inside the sine function.

For a sine function, we have:

`theta(t)=a sin kt` now sub in values to get:

`theta(t)=12sin(pi t)`

**The angle to the vertical is `theta(t)=12sin(pi t)` .**