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Math Help - Trigonometry...test tomorrow!

  1. #1
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    Trigonometry...test tomorrow!

    Hello everyone so I have a math test tomorrow and im stuck on a review question. It's trigonometry in a functions class. I was just wondering if anyone would be able to figure it out.

    heres the question

    1. Given sinx + cosx = 2/3 , calculate the value of sin2x

    any help will be appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by aries View Post
    Hello everyone so I have a math test tomorrow and im stuck on a review question. It's trigonometry in a functions class. I was just wondering if anyone would be able to figure it out.

    heres the question

    1. Given sinx + cosx = 2/3 , calculate the value of sin2x

    any help will be appreciated.
    \sin x + \cos x = \frac 23

    \Rightarrow (\sin x + \cos x)^2 = \frac 49

    \Rightarrow \sin^2 x + 2 \sin x \cos x + \cos^2 x = \frac 49

    can you continue?
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  3. #3
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    I understand how you got to the 3rd step however i still don't know what to do after that. Do I factor it? or is there an identity that I need to use to continue?

    -thanks
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  4. #4
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    The double angle formula states that sin2x = 2*sinx*cosx. That may be helpful along with another trig identity. I suggest memorizing these. If its anything like my highschool trig classes, you will be using them a lot. Many problems can be solved by using a well defined procedure for that given class of problems, combined with a trick. Many students know the procedure but have trouble finding the trick. In this case, I would consider the identities the trick.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sixstringartist View Post
    The double angle formula states that sin2x = 2*sinx*cosx. That may be helpful along with another trig identity. I suggest memorizing these. If its anything like my highschool trig classes, you will be using them a lot. Many problems can be solved by using a well defined procedure for that given class of problems, combined with a trick. Many students know the procedure but have trouble finding the trick. In this case, I would consider the identities the trick.
    right you are.

    @ aries: the other identity you MUST know is \sin^2 x + \cos^2 x = 1

    now can you continue?
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  6. #6
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    great! I'm pretty sure I can finish it now.
    thanks for the help. to both of you.
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