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Math Help - Turning asinx+bcosx to a multiplication.

  1. #1
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    Tirana, Albania
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    Turning asinx+bcosx to a multiplication.

    Hi everyone.
    I have been absent the past week in school because I was ill and I missed a about 5 days worth of new stuff that my classmates learned in maths. I also missed the exam for the chapter of trigonometry.
    So while I was revising every single page I was absent to, one lesion made me very confused and I am having a hard time understanding. I have to turn "asinx+bcosx" to a multiplication. I am not a native English speaker, so I'll try to translate my book as good as i can. About this, it says:

    Solve the equation: 3sinx-sqroot of3*cosx=3
    First, we divide both parts of the equation by 3, and we get: sinx-(sqrootof3/3*cosx)=1
    which is sinx-tan30*cosx=1, so [sin(x-30)]/cos30=1, so sin(x-30)=cos30=sqroot3/2.
    The angle is 60 degrees and we have x-30=k*360+60 or x-30=k*360+120.
    So in conclusion, we have x=k*360+90 or x=k*360+150
    Sorry if Im making you confused. I don't understand the part in bold. I understand what he did with writing tan30 as Sin30/cos30, but where did the "cosx" go, that was right before this step? The one that is underlined and in narrow letters?

    On the other hand, I have a couple of other exercises that I am not able to solve, due to the absence last week ...
    The first one:
    -Find the highest and the lowest value:
    y=sin3x+ sin(90-3x)
    -Prove that:
    cotan2x+1/sin2x=cotanx
    -Turn this into a form of multiplication (from the lesion that I don't understand):
    cos(x-45) + sin (x+ 45)
    -And the last one: sinx-sqrt2=0 (Solve the equation).

    Thank you very much for your help, would appreciate any assistance.
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  2. #2
    MHF Contributor
    Joined
    Sep 2012
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    Australia
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    Re: Turning asinx+bcosx to a multiplication.

    Hey satycorn.

    I understand that you have been sick or have missed school for another reason, but can you show any ideas or partial attempts for these questions? It's a lot easier for everyone if you do this.
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