Advice from Students
on the trig skills needed for
physics and/or calculus

Last updated: 19 August 2006
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What advice would you give to a student currently taking trig concerning the skills and knowlegdge they need to take with them after they pass the class?

That question was on a pre-announced "quiz" taken by 29 of the 33 students still enrolled in PHY2048 at the end of Fall 2004. This group included 23 of the 24 students who passed the course. (I give the answers from those 23 first, but otherwise the answers are not given in any particular order. My personal favorites are numbers 6, 25, 9, 3, and 2.) The "quiz" was given after 12 weeks of the semester, so the information below represents the views of students who have seen all of basic mechanics (what engineers are expected to remember) and done fairly well on the exams. These students also passed MAC2311 (or, in many cases, MAC2312 or MAC2313) so their comments on what is needed in math classes, as well as physics classes, are well founded. Pay attention to what they have to say!

Bold face or all caps show added emphasis that was in the original. In a few places I insert a clarification in [square] brackets to explain something that the student assumed I would understand but that you might not be familiar with. Regular parentheses were in the original comments. You will see some conflicting advice, including comments I would disagree with, but I present them here in their entirety for your enlightenment. My only editorial comment is that you do not need to know the "special angles" (other than multiples of pi/2) for physics; those comments pertain to what is required for calculus tests. Finally, I did touch up the English grammar of some of the foreign (and not so foreign) students.

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What advice would you give to a student currently taking trig concerning the skills and knowlegdge they need to take with them after they pass the class?

  1. Don't just cram for tests, learn the material. Don't just memorize the steps to solving a problem, rather, attempt to understand and be able to apply the broader concepts. Don't assume that anything can be forgotten once the class is over, it ALL comes back in some form (especially trig identities and vectors). Keep your textbook, its good for a reference in later classes.

  2. All that stuff seems boring, with having to remember odd identities and formulas, maybe even the appearance of a sin, cos, or tan function given certain variables? Well, it is boring. But without that knowledge, you'll go from bored to clueless next semester, without time or an instructor to help you. You won't remember everything, but get all the basics down so you'll be able to catch up quickly if you have to use the info later. Once you start hitting higher math classes, all of those weird rules will finally be useful, so hang in there.

  3. I thought trig was so useless when I was in class taking it. However, now that I have taken physics and [engineering] statics, it seems to me to be the most universally useful form of math that there is. If you plan on going any further in math or science, you have to find a way to retain what you are learning.

  4. Know your basic 6 trig functions and their graphs. Understand the unit circle and how to create each point without simply memorizing it. Obviously, that means know your special angles. It is also very important that you remember the fundamental identities (more important for calc). Without a strong working knowledge in, at least, the above listed items, your chances of succeeding in your future physics, calculus, or engineering courses will be slim to none.

  5. Naturally, every student will not remember everything from trig. I believe the important things to remember will include the special angles and their values, as well as the basic trig identities. Students should also learn well the Pythagorean theorem.

  6. It is not just a class to pass, or a speed bump to calc and physics. You should learn and remember geometry, how to apply it, and work with it because you will use trig all throughout calc and physics.

  7. Know like the back of your hand: values of sine, cosine, tangent on the unit circle; all trig identities, double and half-angle formulas; definitions of sine, cosine, tangent; inverse and reciprocal functions of sine, cosine, and tangent and their boundaries [domains]. I am sure there are more, but these are the basics one must know to succeed. The more proficient one is in trig, the easier it will be for one to grasp concepts and manipulate/simplify equations later on. REMEMBER!! Work smarter, not harder and DON'T PANIC!

  8. You're only required to get a "C" in trig, but go for an "A". Trig seems hard at first, but it is the absolute basics of physics and calc. You must totally understand everything in it or you probably won't pass physics, or calc. I got an "A" in trig, and I'm still having a hard time in physics [this student got an A in physics], so if you get less than an "A", you probably won't pass physics.

  9. I would tell any student taking trig that it is one of the important math classes that they will need to take, especially if they are planning to go to higher math or upper science classes. I have come to believe that everything in trig is worth learning because it is the math we use without thinking, but becomes very valuable when you need it.

  10. It is extremely important to know first hand the basic trigonometric functions, to make a clear distinction between degrees and radians (conversion), in a way to transform the physics problem into a basic math problem.

  11. I would tell them that they should really make sure they understand the course and pass it with an A or B grade. I will tell them to pay attention to the topic dealing with vector components.

  12. Trigonometry students need not only to cram the unit circle, but comprehend it. The sine and cosine curves and the concept of amplitude is very important in order to understand related concepts in physics.

  13. Go ahead and commit all of the various trig identities and the unit circle to your long term memory. Do not just cram the night before a test. You will need these in both physics and calculus. Therefore, if you spend a little bit of extra time now commiting them to your long term memory, it will save you a lot of trouble later.

  14. I would advise them to master the unit circle, paying particular attention to the 60, 45, and 30 degree angles. I would also tell them to know and be able to distinquish the cosine and sine functions and to know how they can derive the tangent from the two functions. It is also important that they master the sides of the right triangle and how one would derive the sine and cosine given a triangle with just an angle and the length[s].

  15. Trig identities are your friends when it comes to calculus; however, all of the right triangle identities concerning sin, cos, and tan combined with the Pythagorean theorem will be most helpful in PHY2048.

  16. It is worth taking time to understand the concept of this course [trig]. It's also really, really helpful to memorize the sin, cos, tan, cot of the special angles. Physics is already hard, so don't make it even harder by ignoring the trig.

  17. I would tell them that they don't necessarily need to remember all the formulas, but understand the ideas and theorems because they come back to haunt you. Once you understand what's going on, the formulas will be no problem.

  18. I would tell students who are currently taking trig to try their best to take the most out of it and try to understand the concept completely. Physics depends on "trig" in a lot of concepts.

  19. My advice would be that they should attend every class meeting and take good notes as well as do every possible homework problem in the book that they can, and redo as many problems as they can in their free time. Though most students won't do this, they should keep their trig book and not sell it back to the book store.

  20. My advice would be to learn the material well the first time, so that when you review, it will sink in and become somewhat permanent. Do not take the course lightly, because it is like the foundation to a building. What you will learn in a following course will build on what you already know from this trig course. So, all in all, just learn the material like the back of your hand.

  21. I would tell them to not just study the stuff enough to do well on the test, but to memorize the information needed because they will need it in the classes to follow. A few of the main things that I would tell them to learn and commit to memory are the trig identities and trig functions.

  22. Definitely need to remember trig identities as well as all types of trig functions and how to use them in finding angles and lengths of sides of triangles.

  23. They should try to understand everything that is taught as much as possible, and they should memorize and retain all of the trig identities.

  24. First, they should clearly remember their geometry background. For trig, it is very important that they understand and apply skills like angle measurements, vectors, trig functions with their inverses, trig identities, the unit circle, the trig function's graphs (especially sin x and cos x), similar triangles, and understand the meaning and use of radians and degrees.

  25. I would tell the student that if they plan on going into calculus or physics, that they had better pay close attention to the material in trig and not just learn what is needed for the tests. Learn it over a long period of time, study earlier and longer so the information is remembered longer and clearer, because the trig information will be needed in physics and calculus.

  26. Keep the knowledge dealing with the difference between radians and degrees, and at least the basics of "sin", "cos", and "tan", including their relationships with each other and the components needed to find them. I struggled because I did not get a good background in trig. Study! Study!! Study!!!

  27. I would advise them to retain as much as they can from the course because they are going to use the unit circle (in radians and degrees) in the next classes if they are going to science or engineering majors. Also, the sum of vectors we learn in trig class is very useful for calculus and physics.

  28. I would tell current trig students to remember how to convert deg to rad and rad to deg as well as trig identities. There is also a fair amount of vectors used in physics and calc III that if not learned in trig, should at least be studied by the student on his/her free time.

  29. I would tell them to remember and know the knowledge of that class because they are going to need it in future classes. It is very important that they know everything up to this point because they are going to be using them [again].

A closing comment:
I am extremely impressed with the insight shown in the comments above, and told the class that the next day. In addition, every faculty member I showed these to has been shocked (I chose that word carefully) to read the very things we wish every student would grasp about learning. I hope I can get some of these students to talk to our trig classes, because we all know that most students don't listen to the faculty when they start "lecturing" about learning concepts.

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Background info:
As part of the reaccreditation process, TCC has developed a Quality Enhancement Plan that places a great deal of emphasis on increasing the learning (meaning retention of knowledge after a student has passed a class) that results from our teaching. My own thesis, presented in a seminar on "Learning and the Concept of Prerequisites", is that many students take a short-term approach to passing tests because they have no idea why they are being required to take a particular course. The cram-and-forget approach used when high schools spend many weeks preparing to take the FCAT or similar tests only makes the situation worse. I have little doubt that students fail to pass physics and calculus after "passing" previous math classes because they only learned the material long enough to pass a test, and my seminar presented much evidence in support of this thesis.

One small part of that evidence was student response to the question "What does it mean when we say that 'trig' is a pre-requisite for calculus or physics?" at the start of PHY2048 in Fall 2004. The vast majority said it meant you had to "take" or "pass" that class, while only a small minority said that it meant you would be expected to actually "know" that material. The correct answer is that we mean that you should know most of trig without any study or review.

As a followup, I repeated that question in a "quiz" given late in the semester to see what the students who had survived the course now thought it meant. (The survey was taken by 29 out of 33 still enrolled from an initial class size of 54.) Most now had a very clear idea of what it meant, and gave detailed answers to it and to a followup question asking what they would tell you to learn in your trig class. Their answers are what you see above. I found them extremely insightful, and hope you do also.

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from James Carr
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