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Math Help - Trigonometric functions

  1. #1
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    Exclamation Trigonometric functions

    Hi!
    In this problem I need to find all real numbers x.
    5sin(x)+cos(2x)=3
    and
    5sin(x)+cos(2x)=6

    Can you help me?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Kluringen View Post
    Hi!
    In this problem I need to find all real numbers x.
    5sin(x)+cos(2x)=3
    and
    5sin(x)+cos(2x)=6

    Can you help me?
    Recall that \cos(2x)=\cos^2x-\sin^2x=1-2\sin^2x.

    Thus, 5\sin x+\cos(2x)=3\implies 5\sin x+1-2\sin^2 x=3\implies2\sin^2 x-5\sin x+2=0

    Let u=\sin x. Then solve 2u^2-5u+2=0, and then find x.

    Do something similar for the second one.
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