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Math Help - Sum and diggerence identities

  1. #1
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    Sum and diggerence identities

    Angles for sum and difference identities?

    how to find the angle of the sum and difference identities
    for example sin 15 =(60-45) form where did the 60 and 45 come from and how did you get them in order to solve the problem
    Why can't we use instead of 60 -45 >>>>>>10 +5?
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  2. #2
    ixo
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    This should be the identity that will solve it..
    \sin(u\pm m) = \sin(u)\cos(m)\pm \cos(u)\sin(m)
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by mj.alawami View Post
    Angles for sum and difference identities?

    how to find the angle of the sum and difference identities
    for example sin 15 =(60-45) form where did the 60 and 45 come from and how did you get them in order to solve the problem
    Why can't we use instead of 60 -45 >>>>>>10 +5?
    Hi mj,

    The reason we want to use 60 and 45 is because they are special angles which we can easily find the trig functions for without using a calculator.

    From the unit circle, you should know that:

    \sin 60=\frac{\sqrt{3}}{2}

    \cos 60=\frac{1}{2}

    \sin 45=\cos 45=\frac{\sqrt{2}}{2}

    Now just substitute these values into your angle difference identity:

    \sin(60-15)=\sin 60 \cos 45 - \cos 60 \sin 45

    And simplify.
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