Trigonometry terminology?
January 17, 2011 1:46 PM Subscribe
Math-terminology mismatch? I'm searching for trigonometry in Philadelphia.
College-level trigonometry needed for a graduate of an art-oriented high school. Now he's a freshman engineering student, and needs trig over the summer. But I can't seem to find a University or even Community College in Philly with trig on its course list. How is this possible? Has trig undergone a name change since I took it in high school? Or does my son really need to return to (a different) high school in order to learn it?
Yeah, at Community College of Philadelphia, it's called Math 162: Precalculus II.
posted by Monsieur Caution at 1:53 PM on January 17, 2011
posted by Monsieur Caution at 1:53 PM on January 17, 2011
It's usually called "precalculus" now. Looking at this list of CCP courses, the course he wants is probably Math 162 there.
posted by madcaptenor at 1:53 PM on January 17, 2011
posted by madcaptenor at 1:53 PM on January 17, 2011
Yep, probably pre-Calc. Often, you'll find Calculus as the basic lower level course with a number like 100 or 150 or something like that. If you look at the syllabus for the course that comes just before it, you'll find trigonometry there.
posted by Ashley801 at 1:53 PM on January 17, 2011
posted by Ashley801 at 1:53 PM on January 17, 2011
I learned Trig in high-school in a class called Geometry. But in the case of CCP, it's Precalc II.
posted by Tomorrowful at 1:58 PM on January 17, 2011
posted by Tomorrowful at 1:58 PM on January 17, 2011
Response by poster: Thank you all for the info, especially the specific course numbers at CCP.
I'm a little confused though, because in his mechanical engineering program he will have had Calc I and II by summer, yet he thinks he needs the trig portion of pre-calc he never got. For the math-literate among you, is this a foolish notion?
posted by citygirl at 2:09 PM on January 17, 2011
I'm a little confused though, because in his mechanical engineering program he will have had Calc I and II by summer, yet he thinks he needs the trig portion of pre-calc he never got. For the math-literate among you, is this a foolish notion?
posted by citygirl at 2:09 PM on January 17, 2011
As a practical matter, no, trig is completely unnecessary for Calculus. It will not help him in Calculus, nor will its lack be noticeable. It's a completely separate thing.
If he needs it for a college requirement though... that's a different issue.
posted by brainmouse at 2:15 PM on January 17, 2011
If he needs it for a college requirement though... that's a different issue.
posted by brainmouse at 2:15 PM on January 17, 2011
It's not foolish at all. I'm a calculus teacher, and I generally assume that students coming into Calc I have a firm grasp if trigonometry. Unfortunately, oftentimes I wouldn't call their grasp firm (so I reinforce some of the trickier ideas for trig in my class), but someone with little to no exposure to trig would certainly be in over their head, and I would probably advise them to switch to precalc, then try Calc I again the next semester. Covering trig before taking calculus is an excellent idea.
posted by MidsizeBlowfish at 2:16 PM on January 17, 2011 [1 favorite]
posted by MidsizeBlowfish at 2:16 PM on January 17, 2011 [1 favorite]
As a practical matter, no, trig is completely unnecessary for Calculus. It will not help him in Calculus, nor will its lack be noticeable. It's a completely separate thing.
I have taught calculus at a large university, and I can assure you that this viewpoint is completely false. It does, however, seem to be frequently held among my students.
posted by AkzidenzGrotesk at 2:18 PM on January 17, 2011 [8 favorites]
I have taught calculus at a large university, and I can assure you that this viewpoint is completely false. It does, however, seem to be frequently held among my students.
posted by AkzidenzGrotesk at 2:18 PM on January 17, 2011 [8 favorites]
After posting and seeing brainmouse's post, (s)he is right. Conceptually, no trig is necessary to learn calculus, but as many of the applications of calculus are geometric in nature, it does tend to come up fairly often in a calculus course.
posted by MidsizeBlowfish at 2:19 PM on January 17, 2011
posted by MidsizeBlowfish at 2:19 PM on January 17, 2011
On whether he needs trig before calculus: a lot of it will depend on what sorts of calculus problems he is doing. Many real-world calc usages (e.g., modeling physical systems) use trig because they contain cyclic functions. If he's planning on using calc in those fields, or if the calc prof draws problems from those areas, then trig will show up within the calculus course.
From my own experience, having a strong grasp of trig identities and substitutions made a huge difference in my ability to solve problems in Calc II. I don't think I used as much trig in Calc I.
posted by philosophygeek at 2:21 PM on January 17, 2011
From my own experience, having a strong grasp of trig identities and substitutions made a huge difference in my ability to solve problems in Calc II. I don't think I used as much trig in Calc I.
posted by philosophygeek at 2:21 PM on January 17, 2011
As a practical matter, no, trig is completely unnecessary for Calculus.
Well, you don't need trig to understand the basic concepts of calculus, but one ends up doing calculus on trig functions a lot, so it ends up being a prerequisite for those parts of the course.
It will not help him in Calculus, nor will its lack be noticeable. It's a completely separate thing.
Its lack will probably be noticeable when the course gets to things like d/dx (sin x) = cos x. I'm pretty sure that will come up in a first-semester calculus class.
posted by dfan at 2:28 PM on January 17, 2011 [2 favorites]
Well, you don't need trig to understand the basic concepts of calculus, but one ends up doing calculus on trig functions a lot, so it ends up being a prerequisite for those parts of the course.
It will not help him in Calculus, nor will its lack be noticeable. It's a completely separate thing.
Its lack will probably be noticeable when the course gets to things like d/dx (sin x) = cos x. I'm pretty sure that will come up in a first-semester calculus class.
posted by dfan at 2:28 PM on January 17, 2011 [2 favorites]
On whether he needs trig before calculus
I think the point is that he'll already have had two classes of calculus before he goes back and fills in the trig. So is it different enough that he needs to learn it (as a future engineer) even assuming his calc was OK?
posted by shelleycat at 2:30 PM on January 17, 2011
I think the point is that he'll already have had two classes of calculus before he goes back and fills in the trig. So is it different enough that he needs to learn it (as a future engineer) even assuming his calc was OK?
posted by shelleycat at 2:30 PM on January 17, 2011
I would think you need some trig for first year engineering statics and dynamics, as both of those courses tend to involve forces being applied on angles and so on.
In general, the more solid the math base, the more time one can spend on learning the new material for the course, rather than both the course material and the math underlying it.
posted by Homeboy Trouble at 2:31 PM on January 17, 2011
In general, the more solid the math base, the more time one can spend on learning the new material for the course, rather than both the course material and the math underlying it.
posted by Homeboy Trouble at 2:31 PM on January 17, 2011
If he is taking Calc I/II now and doesn't understand trigonometric functions, picking up a book on it should be easy enough. The school library probably has old introductory texts. Outline intros are cheap and common. And a used, slightly out of date edition of a high school trig textbook or "technical mathematics" textbook should be fairly cheap as well. Bear in mind that trigonometry is a one semester course frequently taught to 16 year olds. I won't say it's not rocket science, because it does have a lot of applications there. And it might be wise to take the minimum number of hours of other college classes while trying to do this. But it's really not too bad to pick up the essentials of trig that you use in calculus on your own.
posted by Monsieur Caution at 2:36 PM on January 17, 2011
posted by Monsieur Caution at 2:36 PM on January 17, 2011
As a practical matter, no, trig is completely unnecessary for Calculus. It will not help him in Calculus, nor will its lack be noticeable. It's a completely separate thing.
You can't take the derivative of SIN without knowing what CoSIN is and why it is. There is way more to trig than just SOHCAHTOA. Even if you can muddle through first semester calc without trig, Second semester Vector and Third semester multivariable Calculus will rely on it quite heavily.
If hes going to do engineering, and particularly MechE., he will need to know, love, and understand trig in a very special way. It will make his life very much easier to learn the hell out of it sooner rather than later.
To answer the question, yeah, Trig is mostly part of either an advanced algebra or a pre-calculus class. While most of what needs to be known in trig can be memorized easily enough. It's knowing how to manipulate the identities intuitively that is really key.
posted by Pogo_Fuzzybutt at 2:36 PM on January 17, 2011 [4 favorites]
You can't take the derivative of SIN without knowing what CoSIN is and why it is. There is way more to trig than just SOHCAHTOA. Even if you can muddle through first semester calc without trig, Second semester Vector and Third semester multivariable Calculus will rely on it quite heavily.
If hes going to do engineering, and particularly MechE., he will need to know, love, and understand trig in a very special way. It will make his life very much easier to learn the hell out of it sooner rather than later.
To answer the question, yeah, Trig is mostly part of either an advanced algebra or a pre-calculus class. While most of what needs to be known in trig can be memorized easily enough. It's knowing how to manipulate the identities intuitively that is really key.
posted by Pogo_Fuzzybutt at 2:36 PM on January 17, 2011 [4 favorites]
So is it different enough that he needs to learn it (as a future engineer) even assuming his calc was OK?
Yes, trigonometry is at least partially used in nearly every branch of engineering, unless he's going to be a "software engineer" or something.
Trigonometry is lumped in with "pre-calc" because calculus is often done on periodic systems, but they really are two different but inter-related skill-sets.
posted by muddgirl at 2:37 PM on January 17, 2011 [1 favorite]
Yes, trigonometry is at least partially used in nearly every branch of engineering, unless he's going to be a "software engineer" or something.
Trigonometry is lumped in with "pre-calc" because calculus is often done on periodic systems, but they really are two different but inter-related skill-sets.
posted by muddgirl at 2:37 PM on January 17, 2011 [1 favorite]
Oh, god, yes, take it. It's not absolutely necessary for Calc I and II for non-engineers, but he'll be absolutely lost in any number of engineering courses, as well as Physics I and II for engineers.
posted by notsnot at 2:56 PM on January 17, 2011
posted by notsnot at 2:56 PM on January 17, 2011
When I took Calculus II summer of freshman year, we did a chapter on trigonometric substitutions. Apart from knowing that
posted by Nomyte at 3:06 PM on January 17, 2011
- sin, cosin, and tan stand for ratios of the sides of a right triangle
- what their values are at crucial points on a unit circle (π/6 increments), and
- that sin²φ + cos²φ = 1,
posted by Nomyte at 3:06 PM on January 17, 2011
I speak as a nonengineer. On the other hand, a number of my friends in college who majored in biomedical engineering (and ours is reportedly the best program in the nation) started with Calculus I their first semester and did quite well throughout undergrad.
posted by Nomyte at 3:10 PM on January 17, 2011
posted by Nomyte at 3:10 PM on January 17, 2011
I'm an engineer (structural, not mechanical). Trigonometry is essential to every type of engineering I've encountered so far. I can't imagine working as an engineer without knowing trig, and most practicing engineers use software that does the calculus for them.
Your son will likely find the trig class much easier after having taken Calc I and Calc II, and ideally, he would have learned trig before the first two semesters of calculus. It might seem overly easy, but it will definitely be worthwhile.
posted by hootenatty at 3:19 PM on January 17, 2011
Your son will likely find the trig class much easier after having taken Calc I and Calc II, and ideally, he would have learned trig before the first two semesters of calculus. It might seem overly easy, but it will definitely be worthwhile.
posted by hootenatty at 3:19 PM on January 17, 2011
I'm a little confused though, because in his mechanical engineering program he will have had Calc I and II by summer, yet he thinks he needs the trig portion of pre-calc he never got. For the math-literate among you, is this a foolish notion?
How did he take pre-calc without first taking trigonometry in high school? I'm not even sure that this is taught in college, since it's basic. But a community college might teach trigonometry as part of a remedial pre-calculus/preparation class, so that's what you should look for.
Calculus and differential equations are going to involve a lot of integration of trigonometric functions, so he's going to have to understand them pretty well.
However, the good news is that understanding the trigonometry necessary for calculus is simply a lot of rote training, so he should be able to pick it up fairly easily during a summer remedial study.
posted by deanc at 3:27 PM on January 17, 2011
How did he take pre-calc without first taking trigonometry in high school? I'm not even sure that this is taught in college, since it's basic. But a community college might teach trigonometry as part of a remedial pre-calculus/preparation class, so that's what you should look for.
Calculus and differential equations are going to involve a lot of integration of trigonometric functions, so he's going to have to understand them pretty well.
However, the good news is that understanding the trigonometry necessary for calculus is simply a lot of rote training, so he should be able to pick it up fairly easily during a summer remedial study.
posted by deanc at 3:27 PM on January 17, 2011
Response by poster: Mefi comes through again! A little background on my son's situation might be helpful. He's a great student and got an all A's last fall, but had undistinguished prep in his art-oriented high school (Interestingly, his college friends are mostly art students). He took geometry on-line and his math is mostly self-taught. He understood and performed well enough to get 740 on his math SAT and earn a partial scholarship. He is in Physics this semester, Calc 2, Chem II, as well as engineering courses using CAD. I suppose they all do, now.
His interest is primarily on refining and perfecting engineered items, and last week expressed an interest in "industrial design", though I doubt he really knows what that is. He believes he needs a firmer grasp on the math of three-dimensionality and believes it will assist in moving from formulae on paper (or screen) to an object in production.
From the informed opinions above, I gather he would 1) benefit from mastering trig 2)but it's impossible to find a trig-only class in college. I'm thinking an on-line class or a few sessions with a good text and a good tutor might be a solution? Especially if he needs it for physics this semester!
posted by citygirl at 3:59 PM on January 17, 2011
His interest is primarily on refining and perfecting engineered items, and last week expressed an interest in "industrial design", though I doubt he really knows what that is. He believes he needs a firmer grasp on the math of three-dimensionality and believes it will assist in moving from formulae on paper (or screen) to an object in production.
From the informed opinions above, I gather he would 1) benefit from mastering trig 2)but it's impossible to find a trig-only class in college. I'm thinking an on-line class or a few sessions with a good text and a good tutor might be a solution? Especially if he needs it for physics this semester!
posted by citygirl at 3:59 PM on January 17, 2011
If his basic math knowledge is deep enough under his skin to earn a 740 on the SAT, he probably doesn't need a lot of "enrichment" math to succeed. Since he's been so successful with teaching himself math, he can probably do well if he just finds some instructional videos on YouTube. There are a lot, and they're pretty good.
If your son decides to continue taking math, he will get lots more exposure to integrating geometric and algebraic ideas in Calculus III (which is usually a required course for engineers anyway — it connects really well to problems in physics and other hard sciences), Differential Equations, and certainly in the more abstract upper-division courses like Differential Geometry, Calculus on Manifolds, and so on.
He may also try looking for a course in "geometry for computer graphics" or something similar. A course like this should cover the math behind representing 3D objects on a 2D surface and how these representations change as objects rotate, translate, scale, etc. A semester of linear algebra may be required, so he may want to take that as well. It's fun!
posted by Nomyte at 4:20 PM on January 17, 2011
If your son decides to continue taking math, he will get lots more exposure to integrating geometric and algebraic ideas in Calculus III (which is usually a required course for engineers anyway — it connects really well to problems in physics and other hard sciences), Differential Equations, and certainly in the more abstract upper-division courses like Differential Geometry, Calculus on Manifolds, and so on.
He may also try looking for a course in "geometry for computer graphics" or something similar. A course like this should cover the math behind representing 3D objects on a 2D surface and how these representations change as objects rotate, translate, scale, etc. A semester of linear algebra may be required, so he may want to take that as well. It's fun!
posted by Nomyte at 4:20 PM on January 17, 2011
His interest is primarily on refining and perfecting engineered items, and last week expressed an interest in "industrial design", though I doubt he really knows what that is.
Well, erm, that's exactly what industrial design is, so he probably has a pretty good idea. (Just sayin'!)
posted by Sys Rq at 4:21 PM on January 17, 2011
Well, erm, that's exactly what industrial design is, so he probably has a pretty good idea. (Just sayin'!)
posted by Sys Rq at 4:21 PM on January 17, 2011
Response by poster: Sys Rq: You make an excellent point. I am coming from an art background - not ID, obviously - and focused on that aspect. Maybe he's more artistic than I give him credit for!
posted by citygirl at 4:27 PM on January 17, 2011
posted by citygirl at 4:27 PM on January 17, 2011
It IS possible to take a trig-only course in college, like the course that I'm taking right now, but perhaps not at your son's college. FWIW, my course is basically "precalc" split into algebra and trig as 2 separate courses. My school also offers them as a combined course.
posted by asciident at 5:19 PM on January 17, 2011
posted by asciident at 5:19 PM on January 17, 2011
The math SAT was ages ago but I remember it being at a pretty basic level. A 740 score is great but a high SAT has little predictive power for success in engineering math. (The predictive power goes the other way, i.e. a low score is a strong predictor of failure. )
This question feels off-base to me. Calc 2 in an engineering program is heavy stuff. By the time he's through he would have sunk or swam. Did he pass Calc 1? Then he knows trig, or at least gets the basics. If he has trouble or wants to shore up a topic, resources over the summer are better spent on private tutoring. Math grad students are affordable, plentiful, and very knowledgeable. His teaching assistants would probably do it for $30 an hour if he asked.
At a more advanced level there is vector calc and even computer graphics courses that might be applicable to his interests. He should talk to an academic adviser at his school.
posted by PercussivePaul at 6:35 PM on January 17, 2011
This question feels off-base to me. Calc 2 in an engineering program is heavy stuff. By the time he's through he would have sunk or swam. Did he pass Calc 1? Then he knows trig, or at least gets the basics. If he has trouble or wants to shore up a topic, resources over the summer are better spent on private tutoring. Math grad students are affordable, plentiful, and very knowledgeable. His teaching assistants would probably do it for $30 an hour if he asked.
At a more advanced level there is vector calc and even computer graphics courses that might be applicable to his interests. He should talk to an academic adviser at his school.
posted by PercussivePaul at 6:35 PM on January 17, 2011
P.S. he should get into the habit of using the resources at his university such as academic advisers. Frankly they will be able to help him a lot better than you or any of us can, because they'll know his situation and be able to ask him questions and figure out what he really needs.
posted by PercussivePaul at 6:53 PM on January 17, 2011 [3 favorites]
posted by PercussivePaul at 6:53 PM on January 17, 2011 [3 favorites]
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posted by Sys Rq at 1:51 PM on January 17, 2011