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In the displayed Fourier-series setup, $a_1$ is the coefficient for $\cos(t)$, which corresponds to the base frequency of $\frac{1}{2\pi}$ hertz. $a_2$ is the coefficient for $\cos(2t)$, corresponding to $\frac{1}{\pi}$ hertz.

Conditions: The function is represented in the displayed form with cosine coefficients $a_1, a_2, a_3$.; The comparison is about the coefficients multiplying $\cos(t)$ and $\cos(2t)$.

In the displayed Fourier-series setup, $a_1$ is the coefficient for $\cos(t)$, which corresponds to the base frequency of $\frac{1}{2\pi}$ hertz. $a_2$ is the coefficient for $\cos(2t)$, corresponding to $\frac{1}{\pi}$ hertz.

Conditions: The function is represented in the displayed form with cosine coefficients $a_1, a_2, a_3$.; The comparison is about the coefficients multiplying $\cos(t)$ and $\cos(2t)$.

The coefficients $a_1$ and $b_1$ act as weights that tell how much each component is involved in the function. If $a_1$ is much larger than $b_1$, the function has more cosine of $t$ than sine of $t$.

Conditions: The series is being constructed as a weighted sum of sines and cosines.; The coefficients are real-valued.

The coefficients $a_1$ and $b_1$ act as weights that tell how much each component is involved in the function. If $a_1$ is much larger than $b_1$, the function has more cosine of $t$ than sine of $t$.

Conditions: The series is being constructed as a weighted sum of sines and cosines.; The coefficients are real-valued.

If the base period is $2\pi$, the term $\cos(t)$ has a frequency of $\frac{1}{2\pi}$ cycles per second. Doubling the argument to $\cos(2t)$ doubles the frequency, so $\cos(2t)$ has a frequency of $\frac{1}{\pi}$ cycles per second.

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

If the base period is $2\pi$, the term $\cos(t)$ has a frequency of $\frac{1}{2\pi}$ cycles per second. Doubling the argument to $\cos(2t)$ doubles the frequency, so $\cos(2t)$ has a frequency of $\frac{1}{\pi}$ cycles per second.

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