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Trigonometry

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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 -

    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 -

    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 -

    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 -

    i am in my grade 11 and study in asia

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