Results 1 to 9 of 9
Like Tree5Thanks
  • 1 Post By MarkFL
  • 1 Post By ibdutt
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL

Math Help - Find coordinates of point P(t)

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    44

    Find coordinates of point P(t)

    Hi!

    If P(t) has coordinates \left(-\frac{\sqrt{5}}{3},\frac23\right), find the coordinates of the point.

    a. P(t + \pi) \rightarrow \left(\frac{\sqrt{5}}{3},-\frac23\right)
    Quadrant 2: moving by π goes half a circle which ends up in Quadrant 4.

    b. P(-t) \rightarrow \left( \frac{\sqrt{5}}{3},-\frac23 \right)
    I just switch the signs.

    c. P(t - \pi) \rightarrow \left( \frac{\sqrt{5}}{3},-\frac23 \right)
    Moving clockwise from Quadrant 2, ending up in Quadrant 4.

    d. P(-t - \pi) \rightarrow \left(-\frac{\sqrt{5}}{3},-\frac23\right)
    From b., moving clockwise from Quadrant 4, ending up in Quadrant 2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Find coordinates of point P(t)

    Parts b and d are incorrect. Draw a diagram, or think of the trigonometric identities (sine and cosine).
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    44

    Re: Find coordinates of point P(t)

    My first attempt was with a diagram.
    So, with sine and cosine I got the same: cosine of a negative is positive and sine of a positive is positive.
    b. \left(\frac{\sqrt{5}}{3},\frac23\right)

    d. \left( \frac{\sqrt{5}}{3},-\frac23 \right)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    826
    Thanks
    209

    Re: Find coordinates of point P(t)

    Also remember that the relationship between polar coordinates ( rcos theta, r sin theta ) for a point with Cartesian coordinates ( x , y ) is given by
    x = r cos theta and y = r sin theta.
    This may help you in understanding the fundamental principal.
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Find coordinates of point P(t)

    Quote Originally Posted by Unreal View Post
    My first attempt was with a diagram.
    So, with sine and cosine I got the same: cosine of a negative is positive and sine of a positive is positive.
    b. \left(\frac{\sqrt{5}}{3},\frac23\right)

    d. \left( \frac{\sqrt{5}}{3},-\frac23 \right)
    b) You want to use:

    \cos(-t)=\cos(t)

    \sin(-t)=-\sin(t)

    This shows you the x-coordinate is the same, while the y-coordinate is negated.

    On a diagram, you would see the original is a quadrant II angle, the the negative is then a quadrant III angle.

    d) Here you can use:

    \cos(-t-\pi)=-\cos(t)

    \sin(-t-\pi)=\sin(t)

    On a diagram, move half a revolution in the negative direction from part b) to wind up in quadrant I.
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    44

    Re: Find coordinates of point P(t)

    OK, I have got that explanation.

    b. \left(-\frac{\sqrt{5}}{3}, -\frac23\right)

    d.  \left(\frac{\sqrt{5}}{3}, \frac23\right)

    Do you have any other alternatives to explaining P(-t)?
    The others I find straightforward, at least so far.

    The whole P(t) stuff is confusing. Here are two explanations I found in a text:
    The mapping of t into P(t) can be described by positioning a copy of the real line vertically with t = 0 coinciding with the point (1,0) on the unit circle. For any real number t, the point P(t) is obtained by "wrapping" the line around the circle and marking as P(t) the point on the circle that corresponds to the position of t.
    From this I understand, whatever number t is, \left(-\frac{\sqrt{5}}{3}, \frac23\right), you place it on the circle. In this case, the quadrant is 2, so the P(t) goes there. I understand no more.

    The reference number for each of the points is t, so the coordinates of each of the points have the same magnitude as those of P(t). However, the coordinates might be negative.
    Understanding - The values will remain the same, except the signs might change.
    Last edited by Unreal; May 6th 2013 at 01:04 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Find coordinates of point P(t)

    For part b), think of the original angle t landing you in the second quadrant, beginning at (1,0). Now, if you begin there again, but movie in the negative direction the same distance along the unit circle, this time you will end up in the third quadrant. Make sense?
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    44

    Re: Find coordinates of point P(t)

    Quote Originally Posted by MarkFL View Post
    For part b), think of the original angle t landing you in the second quadrant, beginning at (1,0). Now, if you begin there again, but move in the negative direction the same distance along the unit circle, this time you will end up in the third quadrant. Make sense?
    Are we beginning at (1,0)?
    If so, I get it from the perspective of the angle being formed looking the same, just moving in different directions -- it's an obtuse angle.

    What exactly is -t supposed to do? In the same way moving \pi from t suggests we are moving by half a circle counterclockwise.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Find coordinates of point P(t)

    Yes, beginning at (1,0) but moving in the opposite direction.
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: January 13th 2012, 03:01 PM
  2. Find the coordinates of the turning point
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 13th 2009, 11:47 PM
  3. Find coordinates of fixed point if...?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 26th 2008, 06:15 AM
  4. Find Coordinates of Point B
    Posted in the Geometry Forum
    Replies: 3
    Last Post: October 4th 2008, 04:24 AM
  5. Find Coordinates of Point B
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 26th 2008, 05:00 AM

Search Tags


/mathhelpforum @mathhelpforum