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Math Help - trigonometry

  1. #1
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    trigonometry

    Prove that 13 cos x + 3 sin x = 13

    Your help will be much appreciated!

    Thank you
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by hermannjp View Post
    Prove that 13 cos x + 3 sin x = 13

    Your help will be much appreciated!

    Thank you
    You cant prove that it is? But you can prove that you could get it by proving that it is in the range...so we need to see if the max of this function exceeds 13 to test this we use the fact that the max of a function of the form a\cdot{sin(x)}+b\cdot{cos(x)} is \sqrt{a^2+b^2}...and since \sqrt{13^2+3^2}=13.6
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  3. #3
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    Quote Originally Posted by Mathstud28 View Post
    You cant prove that it is? But you can prove that you could get it by proving that it is in the range...so we need to see if the max of this function exceeds 13 to test this we use the fact that the max of a function of the form a\cdot{sin(x)}+b\cdot{cos(x)} is \sqrt{a^2+b^2}...and since \sqrt{13^2+3^2}=13.6
    Oh yes, I better rephrase the question. It actually says 'show that...'
    Except showing it's in the range, is there a way I can somehow get the left hand side of the equation to equal the right? The question is worth five marks and it seems to me they want me to show the working that makes left(13 cos x + 3 sin x) stripped down to 13. 0_0
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