পরিভাষা: ম্যাকলরিন ধারা কী?

Note that $\frac{d}{dx}(\cos(x))$ = $-\sin(x)$, $\frac{d^2}{dx^2}(\cos(x))$ = $-\cos(x)$, $\frac{d^3}{dx^3}(\cos(x))$ = $\sin(x)$, and $\frac{d^4}{dx^4}(\cos(x))$ = $\cos(x)$.

So, the derivatives of the cosine function are pretty clearly cyclic with period 4. Also:

$\cos(0) = 1$, $-\sin(0) = 0$, $-\cos(0) = -1$, and $\sin(0) = 0$.

By the formula for a MacLaurin series, noting that each odd derivative has a value of zero, $\cos(x) =$

$1 - \frac {x^2}{2!} + \frac {x^4}{4!} + \cdots$

A Maclaurin series is simply a Taylor series centered around $x=a$. They are named after Scottish mathematician Colin Maclaurin. (Fun fact: Maclaurin was the man who named Taylor series after Brooke Taylor.) Here is a good resource to learn more about Maclaurin series.