Do I need to study trigonometry before calculus?

[WORLD-HEN]

I am studying calculus on my own, and I just skip everything to do with trigonometry. I have never done trigonometry before(except just the basic ratios), and I was wondering whether you really need to study trigonometry before calculus. I see a lot of trigonometry in my calculus book, and I wonder whether I need to know all that to get any deeper insight. Of course, eventually I will do trigonometry, but do I have to before calculus?

 

[motai]

I am studying calculus on my own, and I just skip everything to do with trigonometry. I have never done trigonometry before(except just the basic ratios), and I was wondering whether you really need to study trigonometry before calculus. I see a lot of trigonometry in my calculus book, and I wonder whether I need to know all that to get any deeper insight. Of course, eventually I will do trigonometry, but do I have to before calculus?

Calculus does use a bit of trigonometry, so I wouldn't skip over it altogether. Anyways, some of the trigonometry helps reinforce the concepts learned in calculus. For instance, taking the derivative of sin 2x requires both knowledge of differentiating trigonometry functions (d/dx[sin x]=cos x) and also applied chain rule (2x as u) thus yielding 2 cos 2x. Of course, it can get far more complicated than this, but it shouldn't be too difficult of a problem if you have the right mindset.

When studying the basics of differentiating basic trigonometric functions, feel free to graph them and analyze the extrema, there are correlations worth noting (forgot exactly which ones they are but I know that the zeros of the cos graph [which is the derivative of the sin] are the maximums of the sin graph). Also, note rates of change and visible inflection points on the graphs to help reinforce the concept.

Right now I am working on derivatives of inverse trigonometric functions (arcsin, arccos, etc.) and I have to get used to working them out.

I would recommend at least learning the basics of trigonometric identities, functions, and how to take derivatives of them. There are many problems in my calc book that have some sort of trigonometry in them, and sometimes they combine trigonometry with other things such as logarithmic differentiation/integration and multiple iterations of chain rule .

 

[danne89]

Trig is quite essensial to all elementary science nowadays. You can get pass calc without it, I think. But you'll eventually need it for applied calculus. Anyway trig is easy and shouldn't take so much of your important time.

 

[robert Ihnot]

I did not have any trouble learning a little trig when i studied the Calculus.

 

[mathwonk]

calculus is a technique that applies to any functions. it does not USE trig, rather if you know calculus you can apply it to understand trig functions better.

there are several important classes of functions to which we want toa pplythe ideas of calculus. these are usually polynomials, trig functions, and exponential and log functions.


calculus is very easy to apply to, polynomials, indeed one does not to understand limits at all to apply calculus to them, everything can be done by algebra, musing the explicit formulas they have.

the first inetersting, i.e. mroe difficult functions we try to apply calculus to, are trig functions, because they do not have simple formulas. In fact trig functions cannot even be rigorously defined without suing calculus, because sin and cosine are actually inverse functions of arclength, which requires calculus for its very definition.

after applying the ideas of calculus to trig, a wonderful thing happens: after the fact, one can actualkly write down simple, but infinite, formulas for the trig functions and hence understand them much better than before.

trig functions are important because there are circles in the world which we want to straighten out and measure. I.e. they are relevant to measuring circular arc length.


calculus is useful aprtly becaue it helps us understand important functions, like trig functions and exponential functions, which are even harder to define without calculus.


i.e. the best way to define natural log, is as an area function, for which again calculus is needed.

 

[drdolittle]

read this book..." calculus and analytic geomentry" by thomas/finny...This books provides a good mix of the elements for calculus.

 

[saltydog]

I am studying calculus on my own, and I just skip everything to do with trigonometry. I have never done trigonometry before(except just the basic ratios), and I was wondering whether you really need to study trigonometry before calculus. I see a lot of trigonometry in my calculus book, and I wonder whether I need to know all that to get any deeper insight. Of course, eventually I will do trigonometry, but do I have to before calculus?

Sorry to hear that. That ain't happin' meaning you won't get good in Calculus until you know algebra and trig like the back of your hand. You need to go out of your way to first study trig.

Salty

 

[Manchot]

It's not that the trig functions are isolated, either. Wanna try integrating 1/(1+x^2)? Doesn't look like it would involve trig, would it? Well, it does, and this is only a trivial example. See, here's the thing: the trig functions are intimately tied to exponentials through Euler's formula, which is tied to the natural logarithm through the fact that they're inverses, which is tied to 1/x, etc... Basically, the only treatment of calculus that you can really do without trig functions is the calculus of polynomials, which isn't very interesting.