How to remmember these trigonometric formulas

[estu2]

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

sum to product formulas part

i am looking for a logical way of remmembering them

 

[Count Iblis]

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

sum to product formulas part

i am looking for a logical way of remmembering them

Do not memorize these formulas, it is a bad habit to memorize so many basic formulas. What you should do instead is to memorize only a few basic formulas and then train yourself to be able to derive most of the formulas on that page within one minute.

E.g. I only use these formulas:

sin^2(x) + cos^2(x) = 1

sin(2x) = 2 sin(x) cos(x)

cos(2x) = 2 cos^2(x) - 1

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

cos(x+y) = cos(x)cos(y) - sin(x)sin(y)


Then, if I want to write sin(a) + sin(b) in a product form, I look at the formula

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)


and I then immediately see that you need to consider
sin(x+y) +sin(x-y) after which you can put a = x+y and b = x - y. So, we have:

sin(a) + sin(b) = 2 sin[(a+b)/2]cos[(a-b)/2]

I can do this in 15 seconds in my head, so why on Earth would I want to remember this and the other formulas?

 

[tiny-tim]

sum to product formulas part

i am looking for a logical way of remmembering them

Hi estu2!

Yes, you do need to memorise these formulas.

I remember it this way:

Sum or difference of sin always has a cos and a sin, just as in sin(A±B).

Sum or difference of cos always has two coses or two sines, just as in cos(A±B).

And a sum doesn't depend on the order, so it has to have cos the difference, which also doesn't; while a difference does, so it has to have sin the difference, which also does.