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Math Help - [SOLVED] solve using CAST rule

  1. #1
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    [SOLVED] solve using CAST rule

    Hi,
    I was wondering if you could give me some step-by-step instructions for solving for theta here using the CAST rule:
    sin theta = -1/2, and theta degrees is < theta < 360 degrees.
    (the < symbol also has a line underneath it, which i think means equal. sorry, couldn't write it like it on the keyboard, lol)
    i would appreciate any guides you can think of, thank you!
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  2. #2
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    Isn't the "CAST Rule" just an awareness of the sign of the basic trigonometric functions?

    Positive Sine: Quadrants I and II
    Positive Cosine: Quadrants I and IV
    Positive Tangent: Quadrants I and III

    From a Reference Angle point of view, |sin(x)| = 1/2 produces x = 30º(Quadrant I), 150º (Quadrant II), 210º (Qudarant III), or 330º (Quadrant IV).

    Knowing that, in this case, we have sin(x) = -1/2, discard those in Quadrants I and II, since we know the sine to be positive there. This produces x = 210º or x = 330º.
    Last edited by TKHunny; March 18th 2008 at 06:23 PM.
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  3. #3
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    thans tkhunny! How do you know that sin x produced 30 degrees in the 1st quadrant, 150 in the 2nd quadrant, etc.? that's the part i'm not sure about.
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  4. #4
    Senior Member topher0805's Avatar
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    How do you know that sin x produced 30 degrees in the 1st quadrant, 150 in the 2nd quadrant, etc.?
    Do you know how a reference angle works?
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    Isn't the "CAST Rule" just an awareness of the sign of he basic trigonometric functions?

    Positive Sine: Quadrants I and II
    Positive Cosine: Quadrants I and IV
    Positive Tangent: Quadrants I and III

    From a Reference Angle point of view, |sin(x)| = 1/2 produces x = 30º(Quadrant I), 150º (Quadrant II), 210º (Qudarant III), or 330º (Quadrant IV).

    Knowing that, in this case, we have sin(x) = -1/2, discard those in Quadrants I and II, since we know the sine to be positive there. This produces x = 210º or x = 330º.
    Yeah, I have always said A-S-T-C to myself, but never thought of starting from the 4th quadrant to use the word CAST.
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  6. #6
    Senior Member topher0805's Avatar
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    Quote Originally Posted by colby2152 View Post
    Yeah, I have always said A-S-T-C to myself, but never thought of starting from the 4th quadrant to use the word CAST.
    I use the acronym "All Suckers Take Calculus".

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  7. #7
    Senior Member topher0805's Avatar
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    Just think about it this way:

    In quadrant 1: Reference Angle

    In quadrant 2: \pi - Reference Angle

    In quadrant 3: \pi + Reference Angle

    In quadrant 4: 2\pi - Reference Angle
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  8. #8
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    went through the qu. a few times and I got it now
    sinx-1 = 30
    130 + 30 = 210
    360-30=330
    thank you tkhunny and topher!!
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