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Trig Question: Exact value of

  1. Jun 23, 2011 #1
    Trig Question: Exact value of ......

    1. The problem statement, all variables and given/known data

    Find the exact value of:

    sin(11"pi" / 2)

    without a calculator.....

    2. Relevant equations



    3. The attempt at a solution

    I don't understand how to solve this with the unit circle. What is my first step here?? My text book just gives the answer, and not how to solve it.

    THanks for any help!
     
  2. jcsd
  3. Jun 23, 2011 #2
    Re: Trig Question: Exact value of ......

    try converting 11pi/2 into degrees then looking at the unit circle
     
  4. Jun 23, 2011 #3

    eumyang

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    Re: Trig Question: Exact value of ......

    Find the angle in [0, 2π) that is coterminal to 11π/2.

    As an example, if I wanted to find cos(15π/4), I note that
    cos(15π/4) = cos(7π/4)
    and this angle is in [0, 2π), so it's straight forward to evaluate it.
    cos(7π/4) = √2/2

    You'll have to do something similar in your problem.
     
  5. Jun 23, 2011 #4
    Re: Trig Question: Exact value of ......

    If you start at zero and rotate the radius through that angle, where does it end up? (The "exact value without a calculator" is a hint that it will be equal to one of the common angles.)
     
  6. Jun 23, 2011 #5
    Re: Trig Question: Exact value of ......

    Here is what I came up with....Im sure there is a better way of solving this!

    TO convert into degrees, I get 990. So, thats 360 + 360 + 270, which according to the unit circle is (0,-1), so since its sin, the answer will be -1

    That seems like the wrong way of firguring this out.....

    But how does 11pi/2 equate to 3pi/2
     
  7. Jun 23, 2011 #6

    eumyang

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    Re: Trig Question: Exact value of ......

    Read up on coterminal angles in your textbook (assuming you have one).
     
  8. Jun 23, 2011 #7
    Re: Trig Question: Exact value of ......

    11*pi/2

    A quarter revolution in radians of the unit circle is half a pi (since four quarters aka a complete revolution is 2pi)

    Now just start counting :)

    "But how does 11pi/2 equate to 3pi/2"
    One revolution of the unit circle is 2 pi, therefore wherever you are, you can go 2pi around, you end up in the exact same spot. Any n*pi/2 -/+ 2pi = n*pi/2 is exactly the same if used in a trigonometric function
     
    Last edited: Jun 23, 2011
  9. Jun 23, 2011 #8

    vela

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    Re: Trig Question: Exact value of ......

    You can do the same thing without bothering to convert to degrees first. Every time you go around the circle corresponds to [itex]2\pi[/itex], so subtract off multiples of [itex]2\pi[/itex]. What does that leave you?
     
  10. Jun 23, 2011 #9
    Re: Trig Question: Exact value of ......

    Or it could refer to sum, difference, half or double angle identities.:rolleyes:
     
  11. Jun 24, 2011 #10
    Re: Trig Question: Exact value of ......

    Personally, I find the unit circle very helpful, but you could graph the function in an x-y plot (I'm presuming you understand the period of the sin function at least visually).
     
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