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Math Help - Another trigonometric equation

  1. #1
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    Another trigonometric equation

    If I had the equation 2cosx + sinx = 1 then I could express it as
    √5 cos (x-26.6) = 1. I have no problem when it's like this

    However, if it was 2sinx + cosx = 1, how could I do it? would it be
    √5 sin (x - 63.4) = 1?

    If I go further to find the values of x here, I calculate
    sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8, but because it's not under 360 I take that value away and get 36.8.

    So, I said x was 36.8 and 90. Whenever I put these back into the equation though, it doesn't result in 1, it results in two. Does anyone know why this is and can point out where I'm going wrong?
    Thanks if you can help
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  2. #2
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    Quote Originally Posted by db5vry View Post
    If I had the equation 2cosx + sinx = 1 then I could express it as
    √5 cos (x-26.6) = 1. I have no problem when it's like this

    However, if it was 2sinx + cosx = 1, how could I do it? would it be
    √5 sin (x - 63.4) = 1?

    If I go further to find the values of x here, I calculate
    sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8, but because it's not under 360 I take that value away and get 36.8.

    So, I said x was 36.8 and 90. Whenever I put these back into the equation though, it doesn't result in 1, it results in two. Does anyone know why this is and can point out where I'm going wrong?
    Thanks if you can help
    sinA*cosB + cosA*sinB = sin(A+B)
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  3. #3
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    Quote Originally Posted by db5vry View Post
    However, if it was 2sinx + cosx = 1, how could I do it? would it be
    √5 sin (x - 63.4) = 1?
    2\sin x+ \cos x =1

    Let 2 = r \cos y and 1=r \sin y

    r^2 = \sqrt{2^2+1^2}=\sqrt{5}

    \tan y = \frac{1}{2} \Rightarrow y = 26.6^{\circ}

    so it becomes,

    r[\sin x \cos y+\cos x \sin y]=1

    \sin (x+y)=\frac{1}{r}

    \sin (x+26.6)=\frac{1}{\sqrt 5}

    Quote Originally Posted by db5vry View Post
    If I go further to find the values of x here, I calculate
    sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8 (HOW?)(It should be 386.6), but because it's not under 360 I take that value away and get 36.8 (HOW?).
    Did you get your mistake now??
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