Posted by Tommy on .
How to memorize the sumtoproduct and producttosum 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, ab, i always get confused. Is there any way to memorize more efficiently??

Trigonometry 
Reiny,
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(AB) = sinAcosB  cosAsinB
In the cosine formula, the signs are opposite, that is
cos(A+B) = cosAcosB  sinAsinB and
cos(AB) = cosAcosB + sinAsinB
Write them down a few times, keep the order A,B always in that order, and also say them outloud
Sine ... sincos cossin
cosine .... coscos sinsin
for sines, signs stay the same,
for cosine, signs switch 
Trigonometry 
Tommy,
well, i think u have mistaken my question.
what i meant is i cant memorize the sumtoproduct 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,
I am usually pretty oldfashioned in my mathematical outlook, but in this case for these 12 formulas, I would not expect my students to memorize these rather lowpriority 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,
i am in my grade 11 and study in asia