Matematika Dasar

# Matematika Dasar
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### Silsilah Bilangan
| Kompleks | | | | | | |
| ---- | --- | --- | ---- | --- | --- | --- |
| Imajiner | Riil | | | | | |
| | Irasional | Rasional | | | | | 
| | | Pecahan | Bulat | | | |
| | | -  + | - | Cacah | | |
| | | | | Nol | Asli | |
| | | | | |Ganjil | Genap |
---
### Operasi Penjumlahan
| 1. Komutatif | `$$a+b=b+a$$` |
| --- | --- |
| 2. Asosiatif | `$$a+b+c=(a+b)+c$$` |
| 3. Identitas | `$$a+0=a$$` |
| 4. Inverse | `$$a+(-a)=0$$` |
---
### Operasi Perkalian
| 1. Komutatif | `$$a \times b=b \times a$$` |
| --- | --- |
| 2. Asosiatif | `$$a \times b \times c=(a \times b) \times c$$` |
| 3. Identitas | `$$a \times 1=a$$` |
| 4. Resiproks | `$$a \times \frac 1 a=1$$` |
---
### Pemangkatan
| `$$a \times a \times a=a^{3}$$` |
| --- |
| `$$\frac 1 a \times \frac 1 a \times \frac 1 a=a^{-3}$$` |
| `$$a^{m} \times a^{n}=a^{m+n};(a^{m})^n =a^{mn}$$` |
| `$$a^{0}=1$$` |
---
### Notasi Ilmiah
`$$a \times 10^{b}; 1 \le a \lt 10$$`
### Harga Mutlak
`$$\begin{split}|x|&=x;x \gt0\\&=-x;x \lt0\end{split}$$`
---
`$$\begin{vmatrix}a \times b\end{vmatrix}= {\vert a \vert}\times{\vert b \vert}$$`
`$$\begin{vmatrix}\dfrac a b\end{vmatrix}=\frac {\vert a \vert}{\vert b \vert}$$`
`$$\begin{vmatrix}a^b\end{vmatrix}=a^b;a=2k;k \in\Z$$`
`$$\vert -a \vert=\vert a \vert$$`
---
### Polinomial
| `$$a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...++a_{2}x^{2}+a_{1}x+a_{0}$$` |
| --- |
| `$$a_n...a_0=koefisien$$` |
---
### Notasi Akar
| `$$\sqrt[n]{a};a=radikan;n=index$$` | |
| --- | --- |
| `$$\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{a\times b}$$` | `$$\frac {\sqrt[n]{a}} {\sqrt[n]{b}}=\sqrt[n]{\frac a b}$$` |
| `$$\sqrt[n]{a^m}=a^{\frac m n}$$` | |
---
### Grafik Fungsi Linear
`$$y=mx+n$$`
Data Hasil Percobaan Hukum Ohm
| No. | V (Volt) | I (mA) |
| --- | --- | --- |
| 1 | 1 | 50 |
| 2 | 2 | 102 |
| 3 | 3 | 151 |
| 4 | 4 | 201 |
| 5 | 5 | 253 |

Hasil Percobaan Hukum Ohm

### Logaritma
`$$\log_a b=c\implies a^c=b$$`
`$$\log_{10} b=\log b$$`
`$$\log_{10} 100=\log 100=2$$`
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`$$\log_{a} a^x=x$$`
`$$\log_{a} (x\times y)=\log_{a}x+\log_{a}y \implies\log_{a} \frac x y=\log_{a}x-\log_{a}y$$`
`$$\log_{a} x^p=p\times\log_{a} x\implies\frac{\log_{a}x}{\log_{a}y}=\log_{x}y$$`
`$$\log_{a} a=1\implies\log_{a}1=0$$`
---
### Trigonometri
<img src="../resources/images/tg01.png" width="800" id="id1" onclick="document.getElementById('id1').src = '../resources/images/tg02.png'">
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### Trigonometri
<img src="../resources/images/tg03.png" width="800">
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#### Nilai sin, cos, dan tan sudut istimewa
|  | `$$0\degree$$` | `$$30\degree$$` | `$$45\degree$$` | `$$60\degree$$` | `$$90\degree$$` |
| --- | --- | --- | --- | --- | --- |
| `$$sin$$` | `$$0$$` | `$$\tfrac 1 2$$` | `$$\tfrac 1 2\sqrt2$$` | `$$\tfrac 1 2\sqrt3$$` | `$$1$$` |
| `$$cos$$` | `$$1$$` | `$$\tfrac 1 2\sqrt3$$` | `$$\tfrac 1 2\sqrt2$$` | `$$\tfrac 1 2$$` | `$$0$$` |
| `$$tan$$` | `$$0$$` | `$$\tfrac 1 3\sqrt3$$` | `$$1$$` | `$$\sqrt3$$` | `$$\infty$$`|