At its heart, MATLAB® is a big calculator. To calculate something simply type it in at the "command prompt" and press Enter. Thus, to calculate 1 + 1 we type it in and press Enter. The screen should show:

`>> 1+1 ans = 2`

meaning that the answer is 2.

**Exercise 1.** *Run MATLAB, find the command window and the blinking cursor. Find the answer to the following arithmetic problems:*

- \(1234+4321=?\)
- \(104-765=?\)
- \(47*33=?\)
- \(3^4=?\)
*(The operator for "power" is the circumflex ^, usually found by pressing*Shift ⇑ 6 -
*How far is*\(19^2\)*from its approximation*\(20^2-2*20\)*(Remember that*\((a-b)^2=a^2-2ab+b^2\),*thus the answer should be*±1*)* -
*Find an approximation to*1/73 -
*Find an approximation to*\(\sqrt{31}\)*(while you can of course use the fact that \(\sqrt{x}=x^{0.5}\), you can also "look for" a dedicated function square root by learning how to use the*`lookfor`

*command....)* -
*If you get 5% interest-rate (yearly) on a loan, compounded monthly, and you start with $1000, how much money will you have after 20 years? (don't be confused by an answer of the form*`2.7e3`

*which simply means*\(2.7\times10^3\)*)* *If two sides of a right triangle have lengths 31 and 45, what is the length of the hypotenuse?*

You may have noticed in the exercises that the answer is only given with 5 digits of accuracy (at most). For example, we can ask MATLAB for the value of \(\pi\) and get:

```
>> pi
ans =
3.1416
```

*Internally*, MATLAB keeps a 16 (more-or-less) digit version of the number it shows us, but to keep things orderly, it only displays the answer rounded to show 5 digits (by default). We can change this by issuing a command:

```
>> format long
>> pi
ans =
3.141592653589793
```

We can see this, by subtracting part of \(\pi\) from `ans`

, which always holds the full, unrounded answer to the previous, unassigned expression:

```
>> format short
>> pi
ans =
3.1416
>> ans-3.1415
ans =
9.2654e-05
>> ans - 9.2653e-5
ans =
5.8979e-10
```

**Exercise 2.** *Remember the cosine rule?* \(c^2=a^2+b^2-2a b\, \cos(\theta)\).* Find the length of the hypotenuse of a triangle with angle 30 ^{ο}, and sides with lengths 10 and 20. The* MATLAB

*trigonometric functions*(cos, sin, tan)

*use radians, so you will need to convert using \(\pi\).*

For guided practice and further exploration of how to use the command prompt, watch Video Lecture 2: The Command Prompt.