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How to use the CAST diagram for negative values of x? watch

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    I was never taught this properly, can anyone explain how? I often try to use the conventional graph method but I just end up getting confused when trying to calculate all the other angles in the required range, especially when I'm working with negatives like sinx = -1/2, I can calculate the first angle but I sometimes go wrong with the other angles.

    Also, when questions mention "given that A is obtuse/acute", how am I supposed to use this information?

    Any help much appreciated.
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    (Original post by ElegantElephant™)
    I was never taught this properly, can anyone explain how? I often try to use the conventional graph method but I just end up getting confused when trying to calculate all the other angles in the required range, especially when I'm working with negatives like sinx = -1/2, I can calculate the first angle but I sometimes go wrong with the other angles.

    Also, when questions mention "given that A is obtuse/acute", how am I supposed to use this information?

    Any help much appreciated.
    Basically when it is a positive value, you use it in the all and sin bits and if it is negative then cos and tan. This is for sin x values.
    Similarly, if it was a positive value for tan x, you would use in the all and tan bits and if it was negative then sin and cos.
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    acute = first quadrant
    obtuse = second quadrant
    reflex = third/fourth quadrant
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    (Original post by Deep456)
    Basically when it is a positive value, you use it in the all and sin bits and if it is negative then cos and tan. This is for sin x values.
    Similarly, if it was a positive value for tan x, you would use in the all and tan bits and if it was negative then sin and cos.
    So in drawing the angle I draw it clockwise instead? How about for finding he next angle? Do rotate clockwise or anticlockwise from the first angle? Sorry of this sounds too confusing.
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    (Original post by Pheylan)
    acute = first quadrant
    obtuse = second quadrant
    reflex = third/fourth quadrant
    Oh right haha, I didn't think it was that simple, thanks
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    Well the angles you want will be in the opposite "sections".

    S A
    T C
    ie. With positive X, Sin exists in the top two quadrant. When you're finding negative X, then the angles you want will be in the bottom two quadrants.


    So if you want to find SinX=-0.5, X is -30 from your calculator. Draw this angle onto your CAST diagram. You will find this in the bottom right (C) quadrant. To find the actual angle between 0 and 360, subtract 30 from 360. For the second angle, it should be in the "T" quadrant (bottom left)- thus add 30 to 180.
    If you need more info, just PM/quote me.

    This is easier to visualise if draw this...
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    (Original post by ElegantElephant™)
    So in drawing the angle I draw it clockwise instead? How about for finding he next angle? Do rotate clockwise or anticlockwise from the first angle? Sorry of this sounds too confusing.
    You draw the lines at the angle found from doing inverse of sin x= -1/2 in tan and cos quads. The angles are taken from the horizontal.
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    (Original post by Dichotomy)
    Well the angles you want will be in the opposite "sections".

    S A
    T C
    ie. With positive X, Sin exists in the top two quadrant. When you're finding negative X, then the angles you want will be in the bottom two quadrants.


    So if you want to find SinX=-0.5, X is -30 from your calculator. Draw this angle onto your CAST diagram. You will find this in the bottom right (C) quadrant. To find the actual angle between 0 and 360, subtract 30 from 360. For the second angle, it should be in the "T" quadrant (bottom left)- thus add 30 to 180.
    If you need more info, just PM/quote me.

    This is easier to visualise if draw this...
    That clears things up a bit, thanks
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    (Original post by Deep456)
    You draw the lines at the angle found from doing inverse of sin x= -1/2 in tan and cos quads. The angles are taken from the horizontal.
    Thanks
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    (Original post by ElegantElephant™)
    So in drawing the angle I draw it clockwise instead? How about for finding he next angle? Do rotate clockwise or anticlockwise from the first angle? Sorry of this sounds too confusing.
    To find angles in the positive domain use the anti-clockwise circule.
    To find angles in the negative domain use the clockwise circule.

    P.S: Don't confuse between the sign of an angle and the sign of the value of a trigonometric function.
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    also, find the solution for the whole term, not just for the variable.
    then, find the variable for each solution separately.
 
 
 
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