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Math Help - why is cos(t) -1 as opposed to 1 when P = 3pi

  1. #1
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    why is cos(t) -1 as opposed to 1 when P = 3pi

    find the coordinates of P and the exact values of the trigonomic functions at t whenever possible.

    given

    My answers
    Sin(t) = 0 csc(t)= 1/0 or Undefined
    cos(t) = 1 sec(t) = 1/1 or 1
    tan(t) = 0/1 or 0 cot(t)= 1/0 or Undefined

    The book

    Sin(t) = 0 csc(t)= 1/0 or Undefined
    cos(t) =- 1 sec(t) = - 1/1 or - 1
    tan(t) = 0/1 or 0 cot(t)= 1/0 or Undefined


    Given that the the point is why is cos(t) -1 as opposed to 1?
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  2. #2
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    Quote Originally Posted by rasczak View Post
    Given that the the point is why is cos(t) -1 as opposed to 1?
    Because -3\pi is equivalent to \pi
    Two numbers, t~\&~s, are equivalent if t=s+2n\pi for some integer n.
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  3. #3
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    Quote Originally Posted by rasczak View Post
    find the coordinates of P and the exact values of the trigonomic functions at t whenever possible.

    given

    My answers
    Sin(t) = 0 csc(t)= 1/0 or Undefined
    cos(t) = 1 sec(t) = 1/1 or 1
    tan(t) = 0/1 or 0 cot(t)= 1/0 or Undefined

    The book

    Sin(t) = 0 csc(t)= 1/0 or Undefined
    cos(t) =- 1 sec(t) = - 1/1 or - 1
    tan(t) = 0/1 or 0 cot(t)= 1/0 or Undefined


    Given that the the point is why is cos(t) -1 as opposed to 1?
    Hi rasczak,

    A rotation of \pi radians is an anti-clockwise rotation of 180^o or a half circle.

    A rotation of 2{\pi} is a full circle, back to the starting point.

    Therefore, a rotation of 3{\pi} brings you to the same position that a rotation of \pi does.

    This position is the extreme left of the unit circle.
    The point here is (-1,0).

    The horizontal co-ordinate is Cos(angle) and the vertical co-ord is Sin(angle) for any point on the circumference of the unit circle centred at (0,0).

    If the rotation is done in a clockwise direction, we refer to this using negative angles.

    Hence, a rotation of 3{\pi} ends up at the same position that a rotation of -3{\pi} ends up in.

    This corresponds to an angle \pi
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