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Math Help - Exact value (trig)

  1. #1
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    Exact value (trig)

    How do I find the exact value of an expression like this one?

    u=sin(x+pi/4)

    when sin(x)= 1/3 and x is in the range 0-90 degrees.

    Thanks.
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  2. #2
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    \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}.
    Yeah, that’s what I thought, but what should I do when I have this?

    u=(√2/2)sin(x) + (√2/2)cos(x)
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  4. #4
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    You know that \sin{x} = \frac{1}{3}.

    You should also know that \cos{x} = \sqrt{1 - \sin^2{x}} from the Pythagorean Theorem.

    That means \cos{x} = \sqrt{1 - \left(\frac{1}{3}\right)^2}

     = \sqrt{1 - \frac{1}{9}}

     = \sqrt{\frac{8}{9}}

     = \frac{2\sqrt{2}}{3}.
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  5. #5
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    Allright! Got it now. I assume you mean:

    cos(x)=√1-cos^2(x)

    Which makes:

    cos(x)=√8/3 not √10/3

    That gave me the right answer. Thanks!
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