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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.

The coefficient formula for a Maclaurin series is $c_n = f^{(n)}(0) / n$!. This means the nth coefficient of the power series is found by taking the nth derivative of the function, evaluating it at $x=0$, and dividing by n factorial.

Conditions: The series is expanded around $x=0$.; The function must have derivatives up to order n at 0 for the displayed formula to make sense.; The function is assumed to have a power series representation.

The coefficient formula for a Maclaurin series is $c_n = f^{(n)}(0) / n$!. This means the nth coefficient of the power series is found by taking the nth derivative of the function, evaluating it at $x=0$, and dividing by n factorial.

Conditions: The series is expanded around $x=0$.; The function must have derivatives up to order n at 0 for the displayed formula to make sense.; The function is assumed to have a power series representation.