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Ibnu Sina (980 - 1037 M)

"You know if the object is left unaffected by external influence, it remains as it is". Jika sebuah benda tidak dipengaruhi oleh pengaruh luar maka benda itu akan tetap (seperti kondisi semula).

Abul Barakat Hebattullah bin Malaka (1087-1164)

" The strongest power moves fast and takes a short time. The stronger the power, the faster the power, and the shorter the time. If the power does not decrease, the speed does not decrease, either". In chapter fourteen entitled the Vacuum, he pointed out that "The faster the speed, the stronger the power. The stronger the power that pushes the object, the faster the speed of the object at move, and the shorter the time spent for covering the distance"."In the wrestling arena, everyone has a force practiced against the other. If one of them retreated, this does not mean that his power disappears, but this retreated power still exists, because without it the second one would not need it to influence the first one"

Ibnu Al-Hayytham (965 - 1039)

"The moving object is encountered by an obstruction, and if this forces remains, this moving object retreats in the opposite direction in the same speed practiced by the first object and according to the power of obstruction."

Abdullah Mohamed bin Omar bin Al-Hassan (1150 – 1210)

"The circle pulled by two equal forces until it stops in the middle, it is taken for granted that each forces has practiced an action that obstructs the other"

Showing posts with label Formulasi Matematika. Show all posts

Showing posts with label Formulasi Matematika. Show all posts

DERET

| | Formulasi Matematika

Deret Aritmetika ( $\inline U_{2}-U_{1}=U_{3}-U_{2}=...$ )

$\inline U_{n}=a+\left ( n-1 \right )b$
$\inline S_{n}=\frac{n}{2}\left ( a+U_{n} \right )$
$\inline S_{n}=\frac{n}{2}\left (2a+\left ( n-1 \right )b \right )$
$\inline U_{n}=S_{n}-S_{n-1}$
$\inline U_{t}=\frac{a+U_{n}}{2}$

Deret Geometri $\inline \left (\frac{U_{2}}{U_{1}}=\frac{U_{3}}{U_{2}} \right )$

$\inline U_{n}=ar^{n-1}$
$\inline S_{n}=a\frac{r^{n}-1}{r-1}$
$\inline U_{n}=S_{n}-S_{n-1}$
$\inline U_{t}=\sqrt{aU_{n}}$

Trigonometri

| | Formulasi Matematika

Rumus Trigonometri Pada Segitiga

Untuk Segitiga Sembarang
1. Aturan Sinus

$\inline \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

2. Aturan Cosinus
$\inline a^{2}=b^{2}+c^{2}-2bc \cos A$

Rumus Identitas:

$\inline \sin ^{2}x+\cos ^{2}x=1$

$\inline 1+\tan^{2}x=\sec ^{2}x$
$\inline 1+\cot^{2}x=\csc ^{2}x$

Sudut Ganda
$\inline \sin 2x=2\sin x\cos x$
$\inline \cos 2x=\cos ^{2}x-\sin ^{2}x$
$\inline \cos 2x=2\cos ^{2}x-1$
$\inline \cos 2x=1-2\sin ^{2}x$
$\inline \tan 2x=\frac{2\tan x}{1-\tan ^{2}x}$

Jumlah dan Selisih Sudut
$\inline \sin \left (A+B \right )=\sin A\cos B+\cos A\sin B$
$\inline \sin \left (A-B \right )=\sin A\cos B-\cos A\sin B$
$\inline \cos \left ( A+B \right )=\cos A\cos B-\sin A\sin B$
$\inline \cos \left ( A-B \right )=\cos A\cos B+\sin A\sin B$
$\inline \tan \left ( A+B \right )=\frac{\tan A+\tan B}{1-\tan A\tan B}$
$\inline \tan \left ( A-B \right )=\frac{\tan A-\tan B}{1+\tan A\tan B}$

Jumlah dan Selisih Fungsi Trigonometri
$\inline \sin A+\sin B=2\sin \frac{1}{2}\left ( A+B \right )\cos \frac{1}{2}\left ( A-B \right )$
$\inline \sin A-\sin B=2\cos \frac{1}{2}\left ( A+B \right )\sin \frac{1}{2}\left ( A-B \right )$
$\inline \cos A+\cos B=2\cos \frac{1}{2}\left ( A+B \right )\cos \frac{1}{2}\left ( A-B \right )$
$\inline \cos A-\cos B=-2\sin \frac{1}{2}\left ( A+B \right )\sin \frac{1}{2}\left ( A-B \right )$

Perkalian Fungsi Trigonometri
$\inline 2\sin A\cos B=\sin \left ( A+B \right )+\sin \left ( A-B \right )$
$\inline 2\cos A\sin B=\sin \left ( A+B \right )-\sin \left ( A-B \right )$
$\inline 2\cos A\cos B=\cos \left ( A+B \right )+\cos \left ( A-B \right )$
$\inline -2\sin A\sin B=\cos \left ( A+B \right )-\cos \left ( A-B \right )$

Persamaan Kuadrat

| | Formulasi Matematika

Bentuk umum: $\inline ax^{2}+bx+c=0$ , $\inline a\neq 0$
Akar - akar persamaan kuadrat:

$\inline x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

Determinan:

$\inline D=b^{2}-4ac$

Jumlah dan hasil kali akar - akar:

$\inline x_{1}+x_{2}=\frac{-b}{a}$

$\inline x_{1}x_{2}=\frac{c}{a}$

$\inline x_{1}-x_{2}=\frac{\sqrt{D}}{a}$

$\inline x_{1}^{2}+x_{2}^{2}=(x_{1}+x_{2})^{2}-2x_{1}x_{2}$

$\inline \frac{1}{x_{1}}+\frac{1}{x_{2}}=\frac{x_{1}+x_{2}}{x_{1}x_{2}}$

Rumus persamaan kuadrat yang diketahui akar - akarnya a dan b:

$\inline x^{2}+\left ( a+b \right )x+ab=0$

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