Frequency Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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Find the period of

g(t) = 3\cos\left(\frac{\pi t}{5}\right) + 2

1
Identify $B = \frac{\pi}{5}$ . The period is $T = \frac{2\pi}{B} = \frac{2\pi}{\pi/5} = 10$ .
2
The function completes one full cycle every $10$ units.

Answer

T = 10

The period formula

T = \frac{2\pi}{|B|}

applies regardless of amplitude or vertical shift. The coefficient

B

controls horizontal compression or stretching. Here,

B = \pi/5

gives a relatively long period of 10 units.

About Frequency

The number of complete wave cycles passing a fixed point per second, measured in hertz (Hz).

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