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Math Help - Solving trigonometric equations

  1. #1
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    Solving trigonometric equations

    Hello everyone, I have a question

    solve for all degrees and theta if 0 degrees <= theta < 360 degrees

    1. 2sinTHETA=1

    I how its 1/2 and I know they used the unit circle for the answer the answer is 30 + 360k, 150 + 360k(the first part). I want to know were the 360 came from. Why do I need it in my answer? and how can I use this to find out cot, tan, sec, csc, cos?
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  2. #2
    Junior Member toraj58's Avatar
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    sin function is a periodic function that its period is 2\pi it means after 2\pi intervals the curve will be repeated and sin of the angles also will be reapted after one cycle of 2\pi was completed; and after n iterval it can be calculted like this:

    \sin(n2\pi + \theta) = \sin(\theta)
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  3. #3
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    hope this can help

    2sin(x)=1
    sin(x)=1/2
    so your ref angle is 30 or pi/6
    becuase the question give you a domain for the value of x. you can only find answer within this domain. In your case is 1 positive full rotation.

    sin in Q1 and Q2 have + value.
    so your x values are:
    x=30, and x=150

    sin , cos and tan have two + values in 1 positive full rotation.
    sin in Q1 and Q2
    cos in Q1 and Q4
    tan in Q1 and Q3

    if your question ask you find answer from 0<x<90
    you only can have x=30. Not x=150, because it is over the domain.


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  4. #4
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    Oh now I see it. Thanks. But I still don't understand why I have to but a "+ 360" at the end of it.
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  5. #5
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Sherina View Post
    Oh now I see it. Thanks. But I still don't understand why I have to but a "+ 360" at the end of it.
    Ok think of it like this. sin30 and and sin150 equals 1/2

    Now when you add 360k, k being all intergers, your just making a full roatation.

    For example when k is equal to 1 for


    \sin{(30 + 360(1))}= \frac{1}{2}

    Now try k equals 2 and see what you get.

    It has to do with reference angle
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  6. #6
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    Quote Originally Posted by 11rdc11 View Post
    Ok think of it like this. sin30 and and sin150 equals 1/2

    Now when you add 360k, k being all intergers, your just making a full roatation.

    For example when k is equal to 1 for


    \sin{(30 + 360(1))}= \frac{1}{2}

    Now try k equals 2 and see what you get.

    It has to do with reference angle
    What is a reference angle?
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