How to Solve a Terminal Arm Word Problem and Using Latex

[mathdrama]

Would this be an okay way to go about solving the problem? Also, how do I use Latex?

 

[MarkFL]

You have sketched the arm in the correct quadrant. As for the principal angle, you are correct, however I would write:

$$\theta=\pi-\left(\tan^{-1}\left(-\frac{5}{2}\right)+\pi\right)=\tan^{-1}\left(\frac{5}{2}\right)$$

It appears you are to find the values of the primary trigonometric functions of the angle subtended by the arm and the positive $x$-axis. So, you want to use the angle:

$$\beta=\pi-\theta$$

And recall:

$$\sin(\beta)=\sin(\theta)$$

$$\cos(\beta)=-\cos(\theta)$$

$$\tan(\beta)=-\tan(\theta)$$

As far as using $\LaTeX$, check out our excellent tutorial on getting started:

http://mathhelpboards.com/latex-tips-tutorials-56/mhb-latex-guide-pdf-1142.html