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# Terminology
## Cluster Terms
| Phrase | Definition |
| ----------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| agent | A process running in server or client mode. |
| client/node | A Nomad client is responsible for running tasks assigned to it. A client registers itself with servers and watches for work to be assigned. When running the agent, the client may be referred to as a *node*. |
| server | A Nomad server manages all jobs and clients, monitors tasks, and controls which tasks get placed on which nodes. |
| dev_agent | The development agent is an agent configuration that provides useful defaults for running a single node cluster of nomad. |
## Work terms
| Phrase | Definition |
| ------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| task | The smallest unit of work in Nomad. Tasks are executed by task drivers like `docker` or `exec`, which allows Nomad to be flexible in the types of tasks it supports. Tasks specify their required task driver, configuration for the driver, constraints, and resources required. |
| group | A series of tasks that run on the same Nomad client. |
| job | The core unit of *control* for Nomad and defines the application and its configuration. It can contain one or many tasks |
| job_specification/jobspec | A job specification, also known as a jobspec. |
| allocation | An allocation is a mapping between a task group in a job and a client node. When a job is run, Nomad will chose a client capable of running it and allocates resources on the machine for the ask(s) in the task group defined for the job. |

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# Sine/Cosine
![A graph of sine and cosine](./assets/graphsincos.png) ![A graph of sine and cosine](./assets/graphsincos.png)
Given the above graph: Given the above graph:
@ -15,6 +13,8 @@ Given the above graph:
| $y = cos(2x)$ | Horizontal shrink by a factor of 2 | | $y = cos(2x)$ | Horizontal shrink by a factor of 2 |
# Periodic Functions # Periodic Functions
A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a *period*. A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a *period*.
# Sinusoidal Functions # Sinusoidal Functions
A function that has the same shape as a sine or cosine wave is known as a sinusoidal function. A function that has the same shape as a sine or cosine wave is known as a sinusoidal function.
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$$ y = A * \sin(B(x-\frac{C}{B})) $$ $$ y = A * \sin(B(x-\frac{C}{B})) $$
# Tangent
$$ y = tan(x) $$
![Graph of tangent](assets/graphtan.png)
To find relative points to create the above graph, you can use the unit circle:
If $tan(x) = \frac{sin(x)}{cos(x})$, then:
| $sin(0) = 0$ | $cos(0) = 1$ | $tan(0) = \frac{cos(0)}{sin(0)} = \frac{0}{1} =0$ |
| ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- |
| $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $tan(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ |
| $sin(\frac{\pi}{2}) = 1$ | $cos(\frac{\pi}{2}) = 0$ | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$ |
Interpreting the above table:
- When $x = 0$, $y = 0$
- When $x = \frac{\pi}{4}$, $y = 1$
- When $x = \frac{\pi}{2}$, there's an asymptote
Without any transformations applied, the period of $tan(x) = \pi$. Because $tan$ is an odd function, $tan(-x) = -tan(x)$.
# Cotangent
$$ y = cot(x) $$
![Graph of cotangent](assets/graphcot.svg)
To find relative points to create the above graph, you can use the unit circle:
If $cot(x) = \frac{cos(x)}{sin(x)}$, then:
| $sin(0) = 0$ | $cos(0) = 1$ | $cot(0) = \frac{sin(0)}{cos(0)} = \frac{1}{0} = DNF$ |
| ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- |
| $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cot(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ |
| $sin(\frac{\pi}{2}) = 1$ | $cos(\frac{\pi}{2}) = 0$ | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$ |
Without any transformations applied, the period of $cot(x) = \pi$. Because $cot$ is an odd function, $cot(-x) = -cot(x)$.
# Features of Tangent and Cotangent
Given the form $y = A\tan(Bx - C) + D$ (the same applies for $\cot$)
- The stretching factor is $|A|$
- The period is $\frac{\pi}{|B|}$
- The domain of $tan$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + {\pi}{|B|}k$, where $k$ is an integer. (everywhere but the asymptotes)
- The domain of $cot$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer (everywhere but the asymptotes)
- The range of both is $(-\infty, \infty)$
- The phase shift is $\frac{C}{B}$
- The vertical shift is $D$
# Examples
> Given $-2\tan(\pi*x + \pi) - 1$
$A = -2$, $B = \pi$, $C = -\pi$, $D = -1$
| Transformation | Equation |
| -------------- | ------------------------- |
| Stretch | $\|-2\| = 2$ |
| Period | $\frac{\pi}{\|\pi\|} = 1$ |
| Phase shift | $\frac{-\pi}{\pi} = -1$ |
| Vertical shift | $-1$ |

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@ -32,9 +32,6 @@ C99 adds a `long long` int
## Floats ## Floats
A float is a decimal value. Slower arithmetic and inexact values are both drawbacks of using floats. A float is a decimal value. Slower arithmetic and inexact values are both drawbacks of using floats.
## Characters
In C, a `char` denotes a single byte of arbitrary encoding.
## Variables ## Variables
A variable must be declared before it is assigned. A variable must be declared before it is assigned.