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

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

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Answer 1 · 2016-11-24T16:53:55

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

Explanation:

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Let $T_{1} = the period of the sine function = \frac{2 π}{7}$ $T_1 = "the period of the sine function" = (2pi)/7$
Let $T_{2} = the period of the cosine function = \frac{2 π}{4}$ $T_2 = "the period of the cosine function" = (2pi)/4$

The period for the entire function is the least common multiple of $T_{1} and T_{2}$ $T_1 and T_2$ : $T_{total} = 2 π$ $T_("total") = 2pi$

Here is a graph of the function.
![Desmos.com](useruploads.socratic.org)

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

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

1 Answer

Explanation:

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