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

1 Answer
Nov 24, 2016

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.
Desmos.com

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#