Posted by Tommy on Monday, July 21, 2008 at 7:07am.
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
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 :)
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.
i am in my grade 11 and study in asia