Evaluate sin(theta)

  • Thread starter oddjobmj
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  • #1
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Homework Statement



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

Homework Equations



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

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!
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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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.
 
  • #3
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Wow, way easier than I was letting it be. Thank you!
 
  • #4
Mentallic
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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.
 
  • #5
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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.
 
  • #6
Mentallic
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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.
 
  • #7
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Haha, that makes me feel a little better :P
 

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