What is a good way to understand trig/calculus?

[KamenRiderTorbjorn]

I plan on getting a degree in either computer science or computer engineering, but the issue is I never took a trigonometry or a calculus course yet. What is a good way to understand those subjects?

 

[Vanadium 50]

Work a lot of problems.

 

[e-pie]

Work a lot of problems.

This and conceptual understanding of Calculus, especially the proofs and applications.

 

[Mark44]

In another thread a few months ago you said that you were in a community college. Many four-year CS degree programs have prerequisites of at least calculus, and some require linear algebra and differential equations. Does your college offer a precalculus course? If so, take it, as well as the two-semester/three quarter calculus sequence. The precalc couse very likely covers at least some trig.

 

[symbolipoint]

In another thread a few months ago you said that you were in a community college. Many four-year CS degree programs have prerequisites of at least calculus, and some require linear algebra and differential equations. Does your college offer a precalculus course? If so, take it, as well as the two-semester/three quarter calculus sequence. The precalc couse very likely covers at least some trig.

Pre-Calculus is not enough. Best to be to learn the sequence of courses (which also may have interruptions) Introductory Algebra, Intermediate Algebra. A separate Trigonometry course may also come after or some later time after Intermediate Algebra. A possible continuation of that Algebra series is either "College Algebra", or the combined course called "Pre-Calculus" which is College Algebra And Trigonometry.

Just getting through those courses is not always enough for students to "good way to understand trig/calculus". See what was said in post #2. In each course you should do MORE problem-exercises than just those which were assigned for credit. You also might need to review course material more than once; even AFTER you already earned credit from the course; and again, "work more problems".

That is a good way to understand Trigonometry; and the same idea can work for Calculus.

 

[Mark44]

Pre-Calculus is not enough.

The nomenclature at different schools isn't consistent. Some precalc courses include trig and some don't. Some schools offer precalc I and II, where the latter typically includes trig. At the school where I am currently an adjunct instructor, the relevant classes are called Precalc I: College Algebra and Precalc II: Trig.

 

[verty]

Mark44's school's two classes, College Algebra and Trigonometry, would be very good to take. I am in full agreement on that.

 

[symbolipoint]

The nomenclature at different schools isn't consistent. Some precalc courses include trig and some don't. Some schools offer precalc I and II, where the latter typically includes trig. At the school where I am currently an adjunct instructor, the relevant classes are called Precalc I: College Algebra and Precalc II: Trig.

At least your school gives a dedicated Trigonometry course. It then gives a separate College Algebra course, so your school offers TWO SEPARATE courses, instead of the (where many schools do) the combination College Algebra And Trigonometry (this often being called plainly, Pre-calculus).

If the Algebra sequence or series were offered as college preparatory in high school, these might be called Algebra 1, 2, and 3; but I have never seen College Algebra being called "Algebra 3". What I was aware , there was or maybe still is, a slightly more advanced course in high school called "Trig & Math Analysis". I had such a course a great many years ago. When I studied Pre-Calculus in college, this was much tougher, much more complete, much more advanced than the high school's Trig&MathAnalysis.

 

[symbolipoint]

Another piece of advice, to "Be Good at Trig or Calculus".

Study ahead, and study LONGER in weeks or longer in months. Study on your own more than once. In case one relies on studying a course only while enrolled that course in school, one is potentially limiting his success severely.

Also, study what ever it is that you are doing in your season EVERYDAY!

 

[opus]

For me personally, having just completed College Algebra and Trigonometry, going a little “into the weeds” to know why things are the way they are and the motivation behind them helped me a lot. For example in College Algebra, solving systems of linear equations was pretty confusing until I asked a bunch of questions that led to the realization that you’re really just taking lines or planes and seeing where they intersect simultaneously. These coordinates are thus values that solve each equation in the system simultaneously.

I will also add that to “go into the weeds” requires more study time. When I took these two classes simultaneously and online, I was studying 6 hours a day 5 days a week. But I think that just comes with any math or science class- understating them as best as you can and working problems to drill it in and see where you’re weak.

 

[Mark44]

For example in College Algebra, solving systems of linear equations was pretty confusing until I asked a bunch of questions that led to the realization that you’re really just taking lines or planes and seeing where they intersect simultaneously.

I think that's a key insight -- being able to appreciate the geometry of the situation, instead of merely doing some algebra without little or no understanding of what the equations represent.

 

[opus]

I think so too! Otherwise it feels like arbitrary algebraic steps that you're just told to do so you just do them (at least for me anyways).

 

[symbolipoint]

Drawing a picture, a diagram, or a graph is often ESSENTIAL for understanding, even in Algebra 1; and obviously should be understood as essential in both Trigonometry and Calculus.