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Evaluate sin(theta)

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate cos(θ + π/2) if sin θ = 3/7, exactly.

    2. Relevant equations

    How do I go about doing this exactly instead of approximately on the calculator?

    3. The attempt at a solution

    The only way I know how to do it is taking the inverse sin of 3/7 and adding 90 degrees and taking the cos of that result.

    Thank you for your time!
  2. jcsd
  3. May 8, 2010 #2


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    If sin θ = 3/7 and sin θ = opposite/hypotenuse, can you draw a right angled triangle, with an angle θ, with the opposite side as 3 and the hypotenuse as 7 and find what cosθ is?

    What do you get when you expand out cos(θ + π/2)?

    EDIT: expand out cos(θ + π/2) first and then see what quantities you need to find.
  4. May 8, 2010 #3
    Wow, way easier than I was letting it be. Thank you!
  5. May 8, 2010 #4


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    Or use the fact that [tex]cos(\theta+\pi/2)=-sin\theta[/tex]

    edit: you would probably realise this after expanding the cosine, but if you didn't know how to, using the known graphs of cosx and sinx can give you that result easily.
  6. May 8, 2010 #5
    I appreciate the reference there Mentallic! The issue I'm having is, unfortunately, a lack of time to memorize certain equations and equivalents for an exam.
  7. May 9, 2010 #6


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    Oh yes of course I never expected you to remember this result. I didn't even have this memorised, I had to graph [itex]cos(x+\pi/2)[/itex] to see what it was equivalent to.
  8. May 9, 2010 #7
    Haha, that makes me feel a little better :P
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