Posted by **Tommy** on Monday, July 21, 2008 at 7:07am.

How to memorize the sum-to-product and product-to-sum formulae more easily ??

I know how to deduce the formula but when i try to memorize it, its so hard. Always sin, cos, a+b, a-b, i always get confused. Is there any way to memorize more efficiently??

- Trigonometry -
**Reiny**, Monday, July 21, 2008 at 8:27am
for the sin(A±B) and cos(a±B)

for the Sine is goes sinAcosB ± cosAsinB

and for Cosine is goes cosAcosB ... sinAsinB

for the Sine, the signs stay the same,

that is, sin(A+B) = sinAcosB + cosAsinB and

sin(A-B) = sinAcosB - cosAsinB

In the cosine formula, the signs are opposite, that is

cos(A+B) = cosAcosB - sinAsinB and

cos(A-B) = cosAcosB + sinAsinB

Write them down a few times, keep the order A,B always in that order, and also say them out-loud

Sine ... sincos cossin

cosine .... coscos sinsin

for sines, signs stay the same,

for cosine, signs switch

- Trigonometry -
**Tommy**, Monday, July 21, 2008 at 10:34am
well, i think u have mistaken my question.

what i meant is i cant memorize the sum-to-product formula and product to sum formula, which are

Review

Product to Sum Formulas

1. sin x cos y = (1/2) [ sin(x + y) + sin(x - y) ]

2. cos x sin y = (1/2) [ sin(x + y) - sin(x - y) ]

3. cos x cos y = (1/2) [ cos(x + y) + cos(x - y) ]

4. sin x sin y = (1/2) [ cos(x - y) - cos(x + y) ]

Sum to Product Formulas

1. sin x + sin y = 2*sin[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

2. sin x - sin y = 2*cos[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

3. cos x + cos y = 2*cos[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

4. cos x - cos y = 2*sin[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

1. sin x + sin y = 2*sin[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

2. sin x - sin y = 2*cos[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

3. cos x + cos y = 2*cos[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

4. cos x - cos y = 2*sin[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

Sorry for bothering you again :)

- Trigonometry -
**Reiny**, Monday, July 21, 2008 at 12:56pm
I am usually pretty old-fashioned in my mathematical outlook, but in this case for these 12 formulas, I would not expect my students to memorize these rather low-priority formulas.

Geesh, I even had to look some of these up myself.

I am curious what level of math you are studying and at what college.

- Trigonometry -
**Tommy**, Tuesday, July 22, 2008 at 2:04am
i am in my grade 11 and study in asia

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