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Math Help - Some complex trigo equations

  1. #1
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    Some complex trigo equations

    Hi Guys.

    am stuck with a few trigo questions here ...

    1) Find value of sin10 + sin50 - sin70 without using calculator

    2) Prove that sin(A+2B) + sin(A-2B) = 4sinAsinBcosB

    3) If A =36 , show that sin3A = Sin 2A and find cos 36

    Appreciate your help guys !

    Thanks !
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  2. #2
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    1) Note that 10=30-20, 50=30+20 and 70=90-20. Then think sin(A+B)=sinAcosB+sinBcosA.
    2) Again this is just trig formula sin(A+B)=sinAcosB+sinBcosA and the one for cos as well.
    3) 3A=108 2A=72. Note that 90+18=108 and 90-18=72 and then look at a graph of y=sin(x).
    Let me know how you get on.
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  3. #3
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    Hi Thanks for your help.

    But i kinda dont understand qn 3

    how does looking at the sin curve help me to deduce the value of cos36.
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  4. #4
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    Clarksville, ARk
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    Quote Originally Posted by liukawa View Post
    Hi Thanks for your help.

    But i kinda don't understand qn 3

    how does looking at the sin curve help me to deduce the value of cos36.

    36=2\times 18

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  5. #5
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    sin2A=sin3A
    2sinAcosA=sin(2A+A)
    2sinAcosA=sin2AcosA+sinAcos2A
    2sinAcosA=2sinA\cos^2 A+sinA\cos^2 A -\sin^3 A
    sinA\neq0
    \uptherefore 2cosA=3\cos^2 A - \sin^2 A
    You should now be able to solve this by using trig identities and then applying the quadratic formula.
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