Hey everyone,

I've decided to create a series of daily math problems in order to improve my computer skills. Specifically, these posts will improve my knowledge of gnuplot, HTML, LaTeX, and Maxima. I've chosen to write these posts directly with HTML, even though I could have let WordPress do the HTML automatically. Each daily post contains a few pieces of mathematical text that will require me to use LaTeX, a markup language that has an advantage over HTML due to the fact that it can incorporate mathematical formulae within text. These posts will also help me with my gnuplot and Maxima skills, because they will sometimes contain diagrams and graphs that will accompany the problems.

I started learning gnuplot, HTML, LateX, and Maxima about a week ago, so I will probably make many mistakes. So, feel free to point out all my errors, because I wish to learn from my mistakes!

At first, these problems will be extremely elementary, so I can focus more on using HTML and LaTeX rather than getting bogged down with complexities of the problems. As my HTML and LaTeX skills improve, I'll incorporate harder math problems for your enjoyment. Now, I present to you Problem 1, from Appendix D: Trigonometry of Stewart's *Calculus*, 5e:

**Problem 1:**

A circular arc of length 6 cm is subtended by a central angle of 3π/4. Find the length of the radius of the circle.

*Solution 1:*

*Solution 1:*

In order for us to solve the problem, we will need to know the relationship:

$latex displaystyle theta=frac{a}{r}$

Where *θ* represents the central angle, *a* represents the length of the subtended arc, and *r* represents the length of the radius. We know this relationship holds due to the fact that the subtended arc is proportional to the size of the central angle. Using this relationship, we have *θ* = 3π/4, *a* = 6 cm, and:

$latex displaystyle frac{3pi}{4}=frac{6~text{cm}}{r}$

The use of algebra yields us the result:

$latex displaystyle r=frac{8}{pi}~text{cm}$