## How Much Mathematics Should a Student Memorize?

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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