If the base period is 2π, what frequency does $\cos (2t)$ have?

Conditions

• The base period of the function is $2\pi$.
• The frequency is defined as the reciprocal of the period.

Reasoning, step by step

1. Identify the base frequency of $\cos(t)$ as $\frac{1}{2\pi}$.
2. Recognize that the argument $2t$ implies a period of $\pi$.
3. Calculate the frequency of $\cos(2t)$ as $\frac{1}{\pi}$.
4. Conclude that doubling the argument doubles the frequency.

Example

The speaker says, 'This has a frequency of 1 over 2 pi. This has twice the frequency. This has a frequency of 1 over pi.'

Common misconceptions

• Treating $\cos(2t)$ as just another cosine without recognizing that the 2 changes the frequency.
• Assuming the frequency remains $\frac{1}{2\pi}$ for all harmonic terms.

Watch the explanation

Explore next

• What do the coefficients a₁ and b₁ mean in the series?
• Why does a larger $a_1$ than $a_2$ mean more of the $1/(2π)$ hertz frequency?