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Thread: Simpifying trigonometric expression

  1. #1
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    Question Simpifying trigonometric expression

    Hi,

    I hope someone can help. I'm trying to simplify the following expression:

    Simpifying trigonometric expression-18836578_1422913657764724_462468501_o.jpg

    Apparently the answer is -√3x which is nowhere close to where my steps are going above. I'm curious where I am wrong in my steps?

    Sincerely,
    Olivia
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  2. #2
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    Re: Simpifying trigonometric expression

    Your sum of angles formula for $\sin(\alpha + \beta)$ is wrong.
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    Re: Simpifying trigonometric expression

    Ok I got the right answer after I corrected the formula. Thanks for your help.

    I have one last question. And it is regarding the last two steps before I reach the answer:

    = -sinx(√3/2) - sinx(√3/2)
    = -√3sinx

    I'm curious why you don't add the two sinx's together such that the answer would be -√3 2sinx? I'm going to assume that this is a specific reason behind this that applies to all trig functions, but I would appreciate some specific clarification on this case in particular. I know that the distributive law does not apply to sine function, so maybe that relates to my confusion.
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  4. #4
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    Re: Simpifying trigonometric expression

    it's just combining like terms ...

    $-\dfrac{\sqrt{3}}{2} \cdot \sin{x} - \dfrac{\sqrt{3}}{2} \cdot \sin{x} = -2\left(\dfrac{\sqrt{3}}{2} \cdot \sin{x}\right) = -\cancel{2}\left(\dfrac{\sqrt{3}}{\cancel{2}} \cdot \sin{x}\right)$
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  5. #5
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    Re: Simpifying trigonometric expression

    Quote Originally Posted by otownsend View Post
    Ok I got the right answer after I corrected the formula. Thanks for your help.

    I have one last question. And it is regarding the last two steps before I reach the answer:

    = -sinx(√3/2) - sinx(√3/2)
    = -√3sinx

    I'm curious why you don't add the two sinx's together such that the answer would be -√3 2sinx?
    You seem to be missing the "/2" part! (√3/2)+ (√3/2)= √3, not 2√3.

    I'm going to assume that this is a specific reason behind this that applies to all trig functions, but I would appreciate some specific clarification on this case in particular. I know that the distributive law does not apply to sine function, so maybe that relates to my confusion.
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  6. #6
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    Re: Simpifying trigonometric expression

    Cool. Makes sense. Thank you very much!
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