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Math Help - sin (180 - c) = sin c how ?

  1. #1
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    Exclamation sin (180 - c) = sin c how ?

    i was going through an example in my book and cam across a step
    a + b + c = 180
    a+ b+ = 180 - c
    sin ( a + b) = sin (180 - c) = sin c

    i am not being able to understand how
    sin (180 - c) = sin c
    can anyone please help me?? is it a printing mistake?? thanks in advance
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  2. #2
    Super Member Quacky's Avatar
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    No, it isn't a printing mistake. The sin curve is periodic and fluctuates between -1 and 1 every 360 degrees, causing oscillations which can be divided into symmetrical sections.

    See the graph of y=sin(x) here
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  3. #3
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    Quote Originally Posted by saha.subham View Post
    i was going through an example in my book and cam across a step
    a + b + c = 180
    a+ b+ = 180 - c
    sin ( a + b) = sin (180 - c) = sin c

    i am not being able to understand how
    sin (180 - c) = sin c
    can anyone please help me?? is it a printing mistake?? thanks in advance
    \sin(180-c) = \sin(180)\cos(c) - \cos(180)\sin(c) = (0) \cdot \cos(c) - (-1) \cdot \sin(c) = \sin(c)
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by saha.subham View Post
    i was going through an example in my book and cam across a step
    a + b + c = 180
    a+ b+ = 180 - c
    sin ( a + b) = sin (180 - c) = sin c

    i am not being able to understand how
    sin (180 - c) = sin c
    can anyone please help me?? is it a printing mistake?? thanks in advance
    Another way:
    sin(a - b) = sin(a)~cos(b) - sin(b)~cos(a)

    In your case
    sin(180 - c) = sin(180)~cos(c) - sin(c)~cos(180)

     = (0)~cos(c) - sin(c)~(-1) = 0 - (-sin(c)) = sin(c)

    -Dam
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  5. #5
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    Or- using the "circular definition" of sine, sin(t) is the y coordinate of the point (x, y) an angle t, measured counter-clockwise from the positive x-axis. along the circumference of the unit circle. sin(180- x) would be measured back, clockwise from the negative x-axis. By the symmetry of the circle, those two points have the same y value (and their x coordinates have opposite sign- cos(180- c)= -cos(c)).
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  6. #6
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    does a sketch help?
    Attached Thumbnails Attached Thumbnails sin (180 - c) = sin c how ?-sin-180-c-.jpg  
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