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Math Help - unit circle help

  1. #1
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    unit circle help

    hi, i need a little bit of help with questions such as:

    use a unit circle diagram to find all angles between 0deg and 360deg:

    sine 0.5

    cos 1/root2

    etc...

    i can usually do this as i have a summary of angles of :
    multiples of
    90deg
    45deg
    30deg

    i know what the x and y values are from these.. but when i find the angles i get confused on what angle sine is .. eg with root3/2 i dont know if the angle going anti clockwise is 30 or 60 unless i use my calculator..


    i hope you guys understand what im talking about... as my teacher keeps mentioning the acute angle which i have no idea on where is is ??
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  2. #2
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    Acute means an angle less than 90 degrees.

    The instructions say to use your unit circle diagram... do you have one?
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  3. #3
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    Yes i do have one, but just for test purposes i cant bring one in....
    also i know what acute means but im just wondering where its measured from..

    thanks anyway
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  4. #4
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    Quote Originally Posted by whitestrat View Post
    Yes i do have one, but just for test purposes i cant bring one in....
    also i know what acute means but im just wondering where its measured from..

    thanks anyway
    All angles are measured from the positive x-axis in a counterclockwise fashion.

    Reference angles are measured from either the positive or negative x-axis and are measured in either a clockwise or countclockwise fashion. You can tell if you need to go clockwise or counterclockwise by looking to see what quadrant the angle needs to fall into.

    For example:
    sin(\theta) = -\frac{\sqrt{3}}{2}

    sin(\theta) is the y-coordinate on the unit circle and is negative, so your angle must lie in either the third or fourth quadrants. The reference angle will be an acute angle such that
    sin(\theta) = \left | - \frac{\sqrt{3}}{2} \right | = \frac{\sqrt{3}}{2}

    So the reference angle is 60^o. Since this needs to be in QIII or QIV we get two angles for \theta:
    \theta = 180^o + 60^o = 240^o
    and
    \theta = 360^o - 60^o = 300^o

    -Dan
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