How to memorise exact values for trig? (1 Viewer)

[iStudent]

the neat thing about iStudent's way (the square and square root way) is that it can be applied to any argument. sure you can figure out the acute equivalent of sin(765) but you could also just plug it in and hit the ^2 button LOL

this was my life during hsc maths

Just gotta be wary in case you get "-1/sqrt2" where the negative sign disappears upon squaring. But it still works, just remember to add in the negative sign after.

 

[teridax]

So some here have said that you can just derive via the triangles, yet others say that you must rote learn the exact values for trig. But isn't maths all about grasping the concepts and not rote learning; or does it have to do with 'knowing' niche shortcuts to help you get to the answer?

Because in my opinion, there are some things in maths that you must rote learn.

 

[seanieg89]

So some here have said that you can just derive via the triangles, yet others say that you must rote learn the exact values for trig. But isn't maths all about grasping the concepts and not rote learning; or does it have to do with 'knowing' niche shortcuts to help you get to the answer?

Because in my opinion, there are some things in maths that you must rote learn.

It is good (and indeed efficient) to have basic things like those trig ratios committed to memory, but imo you should NEVER use anything that you can't answer the question "why is this true?" about. It is bad practice, impedes understanding, and this hurts you more the higher level you are studying.

For harder stuff (am talking well beyond the HS syllabus), it is unreasonable to expect people to immediately be able to reconstruct proofs of difficult theorems / the entire procedure of a difficult calculation, but you should still have a rough idea in your head of the key ideas and be able to reconstruct the proofs/calculations with pen, paper and enough time.

 

[Drongoski]

So some here have said that you can just derive via the triangles, yet others say that you must rote learn the exact values for trig. But isn't maths all about grasping the concepts and not rote learning; or does it have to do with 'knowing' niche shortcuts to help you get to the answer?

Because in my opinion, there are some things in maths that you must rote learn.

Wish to comment on "rote learning".

I have noticed that rote learning has a very negative connotation nowadays. In school education, over the last 30 (?) years rote learning has been roundly condemned. It is associated with the "bad" practices of the unenlightened past. The mantra seems to be: rote learning = bad. I'll say that's rubbish! Sometimes rote learning is the most effective way of learning something. But for most situations, especially subjects that require logical reasoning rote learning is not the way. That's why those with poor deductive reasoning skills find the hard disciplines of Maths and Physics (not the dumbed down qualitative-approach NSW HSC version) beyond them. The last 50 years of education, inspite of so much "research" and "progress" in education - I still find education today is not much better than 50 years ago, apart from vast improvements in technology. Nowadays, I observe 90% of students just go for the answers to maths questions; hardly any step-by-step solution. That is not the way to do maths.

As for remembering the exact trig values, you can commit them to memory any way you can; does not have to be rote learning. Commiting to memory is not equal to "rote learning".

As for why it is better to commit to memory if you have a frequent need to use those exact values, it is like having the multiplication table in your head. Nowadays, many many students cannot tell you what 7x8 or 8x9 is; they have to resort to the calculator. What's wrong with this? Well - when you have the table in your head, you are able to see patterns and relationships that those who are calculator-dependent cannot. You are much faster and more efficient. The same goes for remembering the exact trig values. So I always try to get my students to remember the exact trig values but at the same time make sure they can derive them from the triangles if they have forgotten the values.

 

[the_matrix]

There is a trick. Enter the number in the calculator and square that number
so e.g. sin45 = 0.70... square that to get 1/2
So you know the answer is 1/sqrt2

yea this is a method that i used to use until my school banned it LOL

use these triangles:


and you should srsly start memorising them bc in year 11, you have to remember trig identities too which is quite confusing at first unless you use analogies to remember them like i do lol