How to memorise exact values for trig? (2 Viewers)

[tofusenpai]

Is there a technique or like way to make memorising exact values easier?

 

[Silly Sausage]

My teacher made our class memorise it and be able to recall each of them when he randomly asked. If we'd forget he'd give us detention.

 

[D94]

If you are a visual thinker, think of a 30/60 triangle, and a 45 triangle. The 30/60 triangle will have a short side of 1 unit, a perpendicular side of √3 units, and a hypotenuse of 2 units. The 45 triangle will have two 1 unit sides and a √2 unit side.

There's only 6 or so values to memorise. You don't need a technique or any tricks. Do some questions and you will recall them easily over time.

 

[iStudent]

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
Alternatively, just do so many questions that you just recognise straight away that 1/sqrt2 = 0.70... and 1/sqrt3 = 0.866.., sqrt3 = 1.7... etc

*I do not recommend this, since it does slow you down and make you look weird because you're using a calculator for something this basic x)

 

[photastic]

I drew a table and rapped to it.

 

[Trebla]

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
Alternatively, just do so many questions that you just recognise straight away that 1/sqrt2 = 0.70... and 1/sqrt3 = 0.866.., sqrt3 = 1.7... etc

*I do not recommend this, since it does slow you down and make you look weird because you're using a calculator for something this basic x)

This is what I do

 

[Speed6]

I memorised the whole thing. Took me like 3 hours, still remember it now.

 

[Librah]

I still draw the triangles tbh lol.

 

[Drongoski]

I still draw the triangles tbh lol.

You should commit the whole thing to memory. Re-deriving each time from a triangle is too slow. You should have it in your head the way you have the multiplication table in your head. Really - there aren't that many numbers to remember.

 

[Squar3root]

it would be good to remember some of the identities too like sin30 = cos60 = 1/2 to 'cut down' on what you have to memorize

 

[braintic]

sin 00 = √0 / 2
sin 30 = √1 / 2
sin 45 = √2 / 2
sin 60 = √3 / 2
sin 90 = √4 / 2

Reverse for cos

For tan, divide sin by cos:
tan 00 = √0 / √4
tan 30 = √1 / √3
tan 45 = √2 / √2
tan 60 = √3 / √1
tan 90 = √4 / √0

 

[funnytomato]

If you are a visual thinker, think of a 30/60 triangle, and a 45 triangle. The 30/60 triangle will have a short side of 1 unit, a perpendicular side of 2 units, and a hypotenuse of √3 units. The 45 triangle will have two 1 unit sides and a √2 unit side.

There's only 6 or so values to memorise. You don't need a technique or any tricks. Do some questions and you will recall them easily over time.

Personally I remember the triangles, just like for t-results.
Either picture it in mind or just draw it on paper if not sure.

Otherwise for t-results, you have 3 fractions(=6 items) to remember.
And for exact trig ratios, there are many more pieces of information than the two triangles above(which is like 2 pieces of information, for me at least).
I had to work out how to spell "SOHCAHTOA" the other day. Maybe it's just me who learned it in such a weird way.

But it doesn't really matter which method you use, just use the one you find the easiest(I think braintic's discovery is quite neat).

 

[braintic]

(I think braintic's discovery is quite neat).

I'm afraid it's not my discovery. I first read it in some mathematical publication (perhaps 'Parabola') at least 20 years ago. And it keeps getting published so regularly that any maths teacher who does any reading of those types of articles should be aware of it.

 

[Drongoski]

sin 00 = √0 / 2
sin 30 = √1 / 2
sin 45 = √2 / 2
sin 60 = √3 / 2
sin 90 = √4 / 2

Reverse for cos

For tan, divide sin by cos:
tan 00 = √0 / √4
tan 30 = √1 / √3
tan 45 = √2 / √2
tan 60 = √3 / √1
tan 90 = √4 / √0

More or less the same as the one I figured out:



This was in attempt to help some students remember the table. But usually such students are mathematically-challenged, so providing this new schema does not help too much, as they are not too flash with square roots either.

 

[FancyPenguin]

Triangles is easily the best way, just draw them when you need to and your good, or just imagine them in your mind and work of that

http://amsi.org.au/teacher_modules/D4/D4g7.png

 

[integral95]

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
Alternatively, just do so many questions that you just recognise straight away that 1/sqrt2 = 0.70... and 1/sqrt3 = 0.866.., sqrt3 = 1.7... etc

*I do not recommend this, since it does slow you down and make you look weird because you're using a calculator for something this basic x)

If you can get the questions right then who cares

But I reckon that's the fastest way to pull it out if you somehow forgot them.

 

[Drongoski]

Triangles is easily the best way, just draw them when you need to and your good, or just imagine them in your mind and work of that

http://amsi.org.au/teacher_modules/D4/D4g7.png

If you want to be really efficient, in my view, it's not a good idea to derive it each time you need it. Also, when you have those figures in your head, you can see things easily that others can't. So I always urge my students to have the exact values in their head. But, generally, those who are not so good at maths seem to struggle to remember them.

I often wonder: why is it so difficult to remember just 15 values?

 

[futurecompscistudent]

just use your calculator.. I use it all the time HAHAAH

 

[emilios]

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

 

[BLIT2014]

Make a song?