Trig functions and Anki

Trigonometric functions (like sine, cosine, tangent) seem to be perennial in math so I need to go back and master them. I came across them recently in a unit about limits, and even though I have a grasp of the limit concept introduced, my lack of mastery of the trig functions made it impossible for me to pass the quiz. How can I evaluate the limit of e.g. g(x) = sin(x) when x approaches sin(1/pi) without some basic knowledge of this.

I like this, that I came across something now where it’s clear to me that I don’t have the foundation in place. But I know what to do. I’ll go back and study the basics of this particular thing until I master that and then I go back and continue building on the more advanced understanding again.

Another tool I started using for learning is Anki, which is a digital flashcard app. I read an article from Michael Nielsen on using spaced repetition to augment learning (Michael A. Nielsen, “Augmenting Long-term Memory”,, 2018). He argues with some examples that using this spaced repetition style of learning can be useful not only for memorizing facts, but building up understanding in complicated fields like math and science.

I want to leverage this in my math learning. Until now I’ve added two math related cards, and I will add more. The first one was about how it’s possible to evaluate a function f(g(x)) where x approaches some value, and at that value g(x) doesn’t exist. Answer? You can evaluate it from the right and left side of the limit value separately and if they give you the same answer the limit of the full expression does actually exist.

The second one was to learn terminology. What does it mean that two lines are perpendicular to each other? It means that they intersect each other with only right (90 degree) angles. After my recent training session on trig functions I think I will add flashcards to memorize in a unit circle what sin, cos, tan etc. means. And e.g. how does tan relate to cos and sin.

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