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Math Help - Compound Angle Formulas.

  1. #1
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    Compound Angle Formulas.

    Sorry if my post is a bit messy, it's my first

    Question:

    Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.

    a) sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

    So this is the work i've attempted to do so far, I may be completely wrong and once again I apologize for not knowing how to make the pi symbol :

    sin(x+y) = sinx cosy + cosxsiny

    sin(5pi/12 + pi/4) = sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

    sin(5pi/12 + 3pi/12) = sin(pi/4 + pi/6)cos(pi/4) + cos(pi/4 + pi/6)sin(pi/4) *Broke 5pi/12 into pi/4 + pi/6*

    sin(8pi/12) = (sin(pi/4) + sin(pi/6))(cos(pi/4)) + (cos(pi/4) + cos(pi/6)(sin(pi/4))

    sin(2pi/3) = (1/sqr2 + 1/2)(1/sqr2) + (1/sqr2 + sqr3/2)(1/sqr2)

    sqr3/2 =

    sqr3/2 = (1 + 1/2) + (1 + sqr3/2)



    I'm not entirely sure how to cancel stuff out etc. there, and I would like to know if i'm even doing it right. The answer in the back of textbook is sin(5pi/12 + pi/4); sqr3/2
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello kmjt

    Welcome to Math Help Forum!
    Quote Originally Posted by kmjt View Post
    Sorry if my post is a bit messy, it's my first

    Question:

    Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.

    a) sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

    So this is the work i've attempted to do so far, I may be completely wrong and once again I apologize for not knowing how to make the pi symbol :

    sin(x+y) = sinx cosy + cosxsiny

    sin(5pi/12 + pi/4) = sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

    sin(5pi/12 + 3pi/12) = sin(pi/4 + pi/6)cos(pi/4) + cos(pi/4 + pi/6)sin(pi/4) *Broke 5pi/12 into pi/4 + pi/6*

    sin(8pi/12) = (sin(pi/4) + sin(pi/6))(cos(pi/4)) + (cos(pi/4) + cos(pi/6)(sin(pi/4))

    sin(2pi/3) = (1/sqr2 + 1/2)(1/sqr2) + (1/sqr2 + sqr3/2)(1/sqr2)

    sqr3/2 =

    sqr3/2 = (1 + 1/2) + (1 + sqr3/2)



    I'm not entirely sure how to cancel stuff out etc. there, and I would like to know if i'm even doing it right. The answer in the back of textbook is sin(5pi/12 + pi/4); sqr3/2
    I think you've misunderstood the question. You have done all you need (and a whole lot more besides).

    Express as a single trigonometric function:
    \sin(5\pi/12)\cos(\pi/4) + \cos(5\pi/12)\sin(\pi/4)=\sin(5\pi/12+\pi/4)=\sin(2\pi/3)
    and determine the exact value:
    \sin(2\pi/3) = \frac{\sqrt3}{2}
    The phrase 'of each' means, I think, that you do the same for part (b) ..., not to each of the trig functions in the original expression.

    Grandad
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