As Chinese we are good at memorizing poems since young (think of reciting 唐诗300首 – no sweat! ).

By chanting in Hokkien I remember complicated trigo formula:)

Cos 3A = 4Cos^3 A – 3.Cos A

($ 1.3 = $4.3 -$3 with $ =Cos in Hokkien sound).

Once I performed this ‘memory power’ in a lecture hall with me called up by the professor to solve a Physics problem. Halfway in the computation we need to open up the “Cos 3A”, the prof asked the whole class to help me, but I wrote the above down quickly on the white board to the awe of the class. Guess what, when the prof saw it, instead of praising me I got a scolding ! He said “Do not keep unnecessary things in your head”. The prof is a French, he did not know I have Hokkien language advantage… haha.

Anyway, joke aside, try to memorize minimum, go by first principle so that you will never ever forget iin whole life (yes, I remember them now after 40 years).

The more you understand, the less you have to memorize.

A good example is trigonometric identities, of which there are quite a number. Should a student memorize trigonometric identities? Well, at first, it is probably wise to memorize a few of them. Part of a teacher’s job is to help students identify what is essential to memorize, and what is more peripheral. In the case of trig identities, the most important ones are

$latex (1) quad sin^2 theta + cos^2 theta = 1$

$latex (2) quad sin (A pm B) = sin A cos B pm cos A sin B$

$latex (3) quad cos (A pm B) = cos A cos B mp sin A sin B$

Even the $latex pm$ signs are superfluous in equations (2) and (3); one can remember the top signs only, and make use of the symmetry properties of the sine and cosine functions (i.e…

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Pingback: Minimum Memorize in Math – Go by 1st Principle | Math Online Tom Circle

I’m not sure what the “latex” formula is about, but the cos3A formula is fabulous even in English. (My students must have the cos3A formula memorized for a specific test.)

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