I have an expression like this that I need to evaluate:
$$16\sin(2\pi/3)$$
According to my book the answer is $8\sqrt{3}$. However, when I'm using my calculator to get this I get an answer like $13.86$. What I want to know, is it possible to make a calculator give the answer without evaluating $\pi$, so that $\pi$ is kept separate in the answer? And the same for in this case, $\sqrt{3}$. If the answer involves a square root, I want my calculator to say that, I don't want it to be evaluated.
I am using the TI-83 Plus if that makes a difference.
Best Answer
Well we don't need a calculator here. There is no need to write anything in terms of $\pi$.
If you look closely at the sin function you will see that sin$(x) = $ sin$(\pi - x)$.
So sin$(\frac{2\pi}{3}) = $ sin$(\frac{\pi}{3})$.
But what is sin$(\frac{\pi}{3})$?
Well the answer is $\frac{\sqrt{3}}{2}$. You can get this by drawing an equilateral triangle of side length $2$ and splitting in half down the middle (to get a right angled triangle with one angle $\frac{\pi}{3}$ and side lengths $1$, $2$ and $\sqrt{3}$).
So the answer to your question is $16(\frac{\sqrt{3}}{2}) = 8\sqrt{3}$.