# How to remmember these trigonometric formulas

• estu2
In summary, the conversation discusses the use of sum to product formulas in trigonometry and whether or not they should be memorized. The speaker suggests that instead of memorizing all the formulas, it is better to remember a few basic ones and be able to derive the others quickly. They also provide a method for remembering which trigonometric functions appear in sum and difference formulas.
estu2 said:
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?

estu2 said:
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.

## 1. How can I remember the trigonometric formulas?

The best way to remember the trigonometric formulas is to practice using them regularly. You can also try creating mnemonic devices or visual aids to help you remember them more easily.

## 2. Are there any tricks or tips to remember the trigonometric formulas?

One helpful tip is to break down the formulas into smaller parts and understand the meaning behind each part. You can also try creating connections between different formulas to help you remember them better.

## 3. How can I memorize the trigonometric identities?

The best way to memorize the trigonometric identities is to write them down multiple times and repeat them out loud. You can also try practicing with flashcards or creating your own practice problems.

## 4. Is it important to memorize all the trigonometric formulas?

While it is important to have a strong understanding of the trigonometric formulas, it is not necessary to memorize all of them. It is more important to understand how they work and when to use them in different situations.

## 5. Are there any resources available to help me remember the trigonometric formulas?

Yes, there are many online resources, such as practice problems, mnemonic devices, and interactive tutorials, that can help you remember the trigonometric formulas. You can also ask your teacher or classmates for additional study materials.

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