```python
import matplotlib.pyplot as plt
import numpy as np
import sympy
```

# Math Magic: Final Week Review


# Review: A bit of modern math philosophy

### What is the most elementary, simple, basic, primitive kind of math operation?

### What do you call it when you do a bunch of ^that kind of operation in a row?

### What do you call it when you do a bunch of ^that kind of operation in a row?

### Believe it or not, you can keep going down that road. If you do a bunch of ^that in a row, it is called `tetration`!

### A `hyperoperation` 
- The name for any `normal` operation (like the ones above).
- This recursive repeated arithmetic operation can be described by:




# Anyway, that's not even review. Back to the review!




# 1. What is the sine of theta? $sin(\theta) = ?$
# 2. What is the cosine of theta? $cos(\theta) = ?$
# 3. What is the tangent of theta? $tan(\theta) = ?$

# 4. What is the arcsine (inverse sine) of y / r ? $arcsin(\frac{y}{r}) = ?$
# 5. What is the arccosine (inverse cosine) of x / r ? $arccos(\frac{x}{r}) = ?$
# 6. What is the arctangent (inverse tangent) of y / x? $arctan(\frac{y}{x}) = ?$



# 1. What the heck is this demonic drawing above?
# 2. How many $\pi$ radians is 0 degrees?
# 3. How many $\pi$ radians is 90 degrees?
# 4. How many $\pi$ radians is 270 degrees?

# 5. Calculate in python the conversion between any *degrees* angle to *radians*


```python
# YOUR CODE HERE! Try converting degrees to radians 

degrees = 42.42  # convert me to radians!

degrees * (2*np.pi/360)

# HINT: use np.pi, it is a highly accurate pi
```




    0.7403686686959946



# Cowcooloose review


```
                                       /;    ;\
                                   __  \____//
                                  /{_\_/   `'\____
                                  \___ ---(=)--(=)--}
       _____________________________/          :--'
   ,-,'`@@@@@@@@       @@@@@@         \_    `__\
  ;:(  @@@@@@@@@        @@@             \___(o'o)
  :: )  @@@@          @@@@@@        ,'@@(  `===='
  :: : @@@@@:          @@@@         `@@@:
  :: \  @@@@@:       @@@@@@@)    (  '@@@'
  ;; /\      /`,    @@@@@@@@@\\   :@@@@@)
  ::/  )    {_----------------:  :~`, ;
 ;;'`; :   )                  :  / `; ;
;;;; : :   ;                  :  ;  ; :
`'`' / :  :                   :  :  : :
    )_ \__;      ";"          :_ ;  \_\       `,','
    :__\  \    * `,'*         \  \  :  \   *  8`;'*  *
        `^'     \ :/           `^'  `-^-'   \v/ :  \/   -Bill Ames-     
```

### 1. What do we mean by the phrase "rate of change"?
### 2. What do we call the "rate of change" of position?
### 3. What do we call the "rate of change" of velocity/speed?
### 4. What 1-word definition do we use for the phrase "rate of change"?

### 5. What does this thing represent?
## $\frac{df(x)}{dx} = f'(x)$

# Recall that...
## $x(t) = position$
## $\frac{dx(t)}{dt}  = x'(t) = velocity$
## $\frac{dx^2(t)}{dt}  = x''(t) = acceleration$

### 6. The function $f(x) = e^x$ is special for what reason?



# GUESS WHAT



# I THINK



#  WE WILL LEAVE IT AT THAT



# Thank you for a very fun semester!
- I hope you learned something useful!


```python

```

b9a96ed26e5094d1361a778b7e9459e767bec7ea
ipynb
Jupyter Notebook
Math Magic/Week16_FinalWeekWut.ipynb
jonnyhyman/Programming-Classes
f56a9cf90e3b8e4aafad99644f1ed7e87ba14995
MIT
2018-12-15T01:10:51.000Z
2021-07-02T05:23:45.000Z
Math Magic/Week16_FinalWeekWut.ipynb
jonnyhyman/Programming-Classes
f56a9cf90e3b8e4aafad99644f1ed7e87ba14995
MIT
Math Magic/Week16_FinalWeekWut.ipynb
jonnyhyman/Programming-Classes
f56a9cf90e3b8e4aafad99644f1ed7e87ba14995
MIT
2020-02-15T12:47:42.000Z
2021-02-28T03:01:19.000Z
Qwen/Qwen-72B
1. YES
2. YES