As a young college student, we were one of the first classes to do "online" physics problems as homework. The idea was that at the beginning of each week, the professor would hand out 20-25 problems on a sheet of paper. They were all related to the topics being covered during the week. The set was due next Monday. However, these were not to be turned in on paper (this used to be how things were done). Rather, each value was to be input into a customized website. Each student had different numerical values for each problem, so no two sets were alike. This eliminated the ability for students to copy each other outright, which I must admit was a rather nice feature of my high school life.
Many problems in first-year physics involve solving for an angle, either as the final answer, or as some sort of mid-way answer in the problem. This was death for many of my comrades. It was also death for me a few times, although I never had a major problem with it. To solve for an angle, you usually have to use an inverse-trig function. This is essentially a function which "undoes" sine, cosine, or tangent. They are referred to as arcsine, arccosine, and arctangent. So, if you know that the sine of theta is equal to 0.5, then the arcsine of 0.5 gives you the value of the angle.
You have to be certain that the value of this angle makes sense. The advent of the calculator did away with huge sine/cosine tables, but it also automated something that beginner students may not have understood to begin with. That is, the calculator can do trigonometry in two different "modes": radians and degrees.
Somewhere on your calculator there is a wonderful button which toggles between these two modes, and somewhere on your screen there is an indicator of "rad" or "deg". This means that for all sine, cosine, and tangent functions, it is expecting an angle in radians if "rad" is selected, and "degrees" if degrees if "deg" is selected.
If you're not familiar with radians and degrees, I encourage you to take a listen to Episode 011: Radians to Degrees in 2 Steps.
The best piece of advice I can give is when doing any trig function, think about your answer and see if it makes sense. Knowing the angle, you should be able to have a rough idea of your sin/cos value. I encourage you to check out Episode 024: Sines and Cosines by Counting to 4! for more information about guesstimating the value. If what you're seeing on your calculator is way off from this, you're probably in the wrong mode.
When using arcsine, arccosine, arctangent. Think about this value the calculator is showing you. It's supposed to be an angle. 2 pi is somewhere in the range of 6.25. If you're looking for a value in degrees and you have an angle less than 6, either your angle is REALLY small, which 1 in 15 times it is, or you're in the wrong mode. Usually the answer is less than 90 degrees, which is less than 1.5 radians. If the angle is less than 1.5, chances are you're in the wrong mode.
We used to spend a long time going through problems to find out where my friends and sometimes yours truly veered. This was many times just that place. Typing in an angle of 0.2435. The computer doesn't know you're in radians! This brings to mind a wise aphorism from physics teachers across the board: Check Your Units!
For some reason a lot of people don't associate degrees and radians with units. It's a very small detail to lose in the grand scheme, but keeping an eye out for it can save you 20 points on the big test. Don't let them slip through your fingers.
