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Thread: Trigonometric Functions of Real Numbers

  1. #1
    Member purplec16's Avatar
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    Trigonometric Functions of Real Numbers

    Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P.

    $\displaystyle (a)2\pi$ $\displaystyle (b)-3\pi$

    Can someone please help me I dont know what is it that I need to do find the coordinates?
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    Quote Originally Posted by purplec16 View Post
    Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P.

    $\displaystyle (a)2\pi$ $\displaystyle (b)-3\pi$

    Can someone please help me I dont know what is it that I need to do find the coordinates?
    hi purplec16,

    Cos(t) gives you the x co-ordinate of P
    Sin(t) gives you the y co-ordinate of P

    where t are the values given in (a) and (b)
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  3. #3
    Member purplec16's Avatar
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    i still dont really understand what to do
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  4. #4
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    Quote Originally Posted by purplec16 View Post
    i still dont really understand what to do
    you need to learn the unit circle ...

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    Member purplec16's Avatar
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    I mean I did but how will all of that come together to solve my problem?
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  6. #6
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    Using skeeter's neat diagram,

    you need to locate the angles $\displaystyle t=2\pi$

    and $\displaystyle t=-3\pi$

    $\displaystyle 2\pi$ corresponds to zero degrees on the extreme right on the x-axis where the circle touches the axis.

    The co-ordinates are (1,0).

    You can also obtain these by calculating $\displaystyle Cos(2\pi)$ and $\displaystyle Sin(2\pi)$

    The angle $\displaystyle t=-3\pi$ is a negative angle.

    Positive angles are anticlockwise.
    Negative angles are clockwise.
    Angles start from zero or $\displaystyle 2\pi$.

    $\displaystyle -3\pi$ means go $\displaystyle 2\pi$ radians clockwise, then another $\displaystyle \pi$ radians clockwise.

    This causes us to end up at $\displaystyle \pi$ radians.

    You can read off the co-ordinates of this position on the circle,
    or you can use your calculator to calculate $\displaystyle Cos(-3\pi)$ for the x co-ordinate, and $\displaystyle Sin(-3\pi)$ for the y co-ordinate.

    Why not try this and check that the co-ordinates calculated match skeeter's diagram.

    Remember... x=Cos(angle), y=Sin(angle) on the unit circle.
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  7. #7
    Member purplec16's Avatar
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    So, in my math text, they have the answer for a and b as:
    $\displaystyle (a) (1,0); (0,1); (0,U); (1,U)$
    $\displaystyle (b) (-1,0);0,-1;0,U;-1,U$

    How is it that they got those answers?

    U: undefined
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  8. #8
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    There must be more to the question...

    For (a) the point (1,0) are the co-ordinates of zero or $\displaystyle 2\pi$

    (0,1) are the co-ordinates of $\displaystyle \frac{\pi}{2}$

    (-1,0) are the co-ordinates of $\displaystyle \pi$

    (0,-1) are the co-ordinates of $\displaystyle \frac{3\pi}{2}$

    Check your book again for the entire question.
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  9. #9
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    The questions states: Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometic functions of t, whenever possible.

    (a) $\displaystyle 2\pi$ (b)$\displaystyle -3\pi$
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  10. #10
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    Quote Originally Posted by purplec16 View Post
    So, in my math text, they have the answer for a and b as:
    $\displaystyle (a) (1,0); (0,1); (0,U); (1,U)$
    $\displaystyle (b) (-1,0);0,-1;0,U;-1,U$

    How is it that they got those answers?

    U: undefined
    For (a) the first pair in brackets are the co-ordinates (x,y).
    The second pair is (Sin(t), Cos(t))
    The third pair is (Tan(t), Cot(t))
    The fourth pair is (Sec(t), Cosec(t))

    Same situation for (b) corresponding to $\displaystyle t=-3\pi$
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