How Much Trig is Involved in Basic Calculus?

[chez_butt23]

Hi,

I am a biology major starting my freshman fall quarter in about two weeks. I have always struggled with math (mostly due to a lack of effort). However, over the summer, I have made huge strides in my progress as I have been working extremely hard to master algebra and pre-calculus in preparation for the calculus series at have to take this year, but I still seem to struggle with trig. How much trig do I need to know for my "Calculus for Biology Majors" class? We do not cover the same material as the "normal" calculus classes. The chapters from my textbook are as follows:

1.Preview/Review
2.Discrete Time Models, Sequences, and Difference Equations
3.Limits and Continuity
4.Differentiation
5.Applications of Differentiation
6. Integration
7. Integration Techniques and Computational Methods
8. Differential Equations
9. Linear Algebra and Analytic Geometry
10. Multivariable Calculus
11. Systems of Differential Equations
12. Probability

How much trig is involved in these topics at a freshman level?

Thanks.

 

[gb7nash]

It's hard to say without knowing your curriculum/syllabus. This is a question better left for your instructor. My guess (and it's only a guess) is that you need to be pretty familiar with trig. You want to be familiar with what sine, cosine, tangent are in relation to a right triangle, be able to graph trig functions (sin(x),cos(x),tan(x)), and know trigonometric identities. For example, there's a good chance you're going to understand how to integrate functions with the use of a trig identity.

This may not be the answer you want to hear, but I'm going off of what I've seen in a standard calculus class.

 

[Angry Citizen]

From my experience in calculus, you don't really need to learn any more trig identities than the pythagorean identity (sin^2 + cos^2 = 1) and the subsequent divisions through by the trig functions (for instance, dividing through by sin^2 yielding 1 + cot^2 = csc^2). Just know the definitions and a basic idea about the graphs of sin, cos, and tan, and you'll be fine.

 

[HeLiXe]

Too much for my liking -_-
definitely the pythagorean identities and quotient identities...I think the double angle identities are used as well. Calc II makes definite use of the double angle identities and half angle identities.

Edit:
And all the things Angry Citizen said about the graphs and definitions. I remember drawing out things when it came to inverse trig functions and hyperbolic functions.

 

[Chunkysalsa]

What part of trig are you not comfortable with. As long as you are aware of the trig functions and some basic identities (pythagorean) then you'll do fine.

Trig usually comes up more in calc2 stuff (integration) but again not to complicated.

 

[Dembadon]

Well, looking at the chapters in your textbook, it appears as if you have a full, 3-semester textbook. You might only use the first six chapters or so. What is the name and who is the author of your textbook?

How much trig is involved in these topics at a freshman level?

To answer the question directly, there's potentially a lot of trig involved with the topics you've listed. However, I don't think that you'll be using the entire book your freshman year, nor do I believe that biology majors are typically required to take MV Calculus. But without seeing your program or knowing your instructor, I can't say for sure.

Regarding what to know right off the bat -- As others have said, knowing the trig identities will help. Beyond that, I would say it wouldn't hurt to know the exact values of the common angles (π/6, π/4, π/3, ... ).

 

[chez_butt23]

Thanks for the help everyone. To answer some questions, I can easily do some really basic trig, such as pretty much everything on khan academy listed before law of sines. From what I remember, I just really happened to struggle with proofs. Do I need to keep studying, or can I move on to calculus topics, such as limits etc?

 

[mathsciguy]

Thanks for the help everyone. To answer some questions, I can easily do some really basic trig, such as pretty much everything on khan academy listed before law of sines. From what I remember, I just really happened to struggle with proofs. Do I need to keep studying, or can I move on to calculus topics, such as limits etc?

If you are completely new to trigonometry, it's not a bad idea to start with Khan academy as I really found it friendly with beginners. As you learn though, I suggest that you help yourself with a book. With that you can make yourself understand the material in depth (I see Khan Academy no more than an introduction).

If you are having trouble proving, you should familiarize yourself more with the basic identities especially the pythagorean and the sum and difference identities, since this is where the other identities are derived from.

 

[verty]

Well calculus and trigonometry are similar in this sense, they both are about calculating things (that's how I think of them). Calculus is about areas, volumes and rates of change, and trigonometry is about calculating areas, sides and angles of triangles.

So I think that one can handle calculus with the same approach as one handles trigonometry, which is to focus on the techniques that one must learn rather than thinking too much about the theory. The proof of Pythagorous's theorem may be insightful to some but using it is to me what makes it valuable, that it is such a useful theorem. The same is true for those rules in trig, they are all theorems but they are very useful too!

So I think you can take from the trigonometry not necessarily a memorization of the formulas but an appreciation of how they can be useful. Because if you know how to use them, you won't forget them, it's like riding a bike.

 

[HeLiXe]

I think you can move on to limits and come back to trig as needed. A break will probably do your mind good and you can have a better idea of what you will be working with in calc.