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Thread: 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 $\displaystyle 2\pi$ it means after $\displaystyle 2\pi$ intervals the curve will be repeated and sin of the angles also will be reapted after one cycle of $\displaystyle 2\pi$ was completed; and after n iterval it can be calculted like this:

    $\displaystyle \sin(n2\pi + \theta) = \sin(\theta)$
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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


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

    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


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

    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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