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Math Help - trig fourmulas and proofs

  1. #1
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    trig fourmulas and proofs

    Use the addition formulas to find the exact value of the given expression
    1) Cos 11(pi)/12

    2) Sin23 cos37 + cos23 sin37

    FORMULAS:
    sin(u +/- v) = (sin u cos v +\- cos u sin v)
    cos(u +/- v) = (cos u cos v -\+ sin u sin v)
    tan(u +/- v) = (tan u +\- tan v) / (1 -\+ tan u tan v)



    My teacher gave this worksheet and gave the answers and is grading on the work and process... unfortunately i was sick the day we learned how to do these. Any help AND explanation would be greatly apreciated!
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  2. #2
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    Quote Originally Posted by Heather10 View Post
    Use the addition formulas to find the exact value of the given expression
    1) Cos 11(pi)/12

    2) Sin23 cos37 + cos23 sin37

    FORMULAS:
    sin(u +/- v) = (sin u cos v +\- cos u sin v)
    cos(u +/- v) = (cos u cos v -\+ sin u sin v)
    tan(u +/- v) = (tan u +\- tan v) / (1 -\+ tan u tan v)



    My teacher gave this worksheet and gave the answers and is grading on the work and process... unfortunately i was sick the day we learned how to do these. Any help AND explanation would be greatly apreciated!
    (1) error made, see below post

    (2)Use the sin addition formula :

     <br />
Sin23 cos37 + cos23 sin37=sin(23+37)=sin60=\frac{\sqrt{3}}{2}<br />
    Last edited by Jameson; March 3rd 2009 at 10:00 PM. Reason: indicating poster's error
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  3. #3
    MHF Contributor
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    Sorry i made a mistake for (1)

    cos\frac{11\pi}{12}=cos\frac{11}{12}(180)=cos165=-cos15

    Perhaps you are not allowed to use the calculator to do this :

    -cos15=-cos\frac{1}{2}(30)

    Use this identity :

    cos\frac{a}{2}=\sqrt{\frac{1+cosa}{2}} where a=30 .
    Last edited by mathaddict; March 3rd 2009 at 10:08 PM.
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