Question

What is the period of `f(theta)= sin 7 t - cos 2 t`?

Answer 1

The period is least common multiple of the two periods: `2pi`

Explanation:

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Let `T_1 = "the period of the sine function" = (2pi)/7`
Let `T_2 = "the period of the cosine function" = (2pi)/4`

The period for the entire function is the least common multiple of `T_1 and T_2`: `T_("total") = 2pi`

Here is a graph of the function.

Please notice the zero at `x = (5pi)/18`; the pattern surrounding that zero repeats, again, at `x = (41pi)/18`. That is a period of `2pi`