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Math Help - Introduction to circular functions.

  1. #1
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    Introduction to circular functions.

    determine the value of the following if theta degrees is less than or equal to theta and theta is less than 360. note:2 values for each

    sec theta= -root2




    cot theta= infinite


    note: i have just been having troubles with the reciprocal stuff.
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  2. #2
    Super Member Matt Westwood's Avatar
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    "reciprocal" of anything is "1 divided by" that anything.

    And "sec theta" is the reciprocal of "cos theta".

    So "sec theta = - root 2" is the same thing as "cos theta = 1 / (-root 2)".

    1 /root 2 is one of those well-known ones, cos theta = 1 / root 2 means that theta = 45 degrees.

    But it's minus, so you have to go into the 2nd or 3rd quadrant (where x is negative) which gives theta as 135 or 225 degrees.

    Now cot theta = infinite.

    Cot theta is the reciprocal of tan theta, so cot theta = infinite is the same as tan theta = 1 / infinite which is zero.

    (No complicating arguments about what this "means" - we're in basic stuff here.)

    So we have tan theta = 0 which means theta = 0 or theta = 180 degrees.

    Hope this helps.
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  3. #3
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    Quote Originally Posted by Dave19 View Post
    determine the value of the following if theta degrees is less than or equal to theta and theta is less than 360. note:2 values for each

    sec theta= -root2




    cot theta= infinite


    note: i have just been having troubles with the reciprocal stuff.
    You call them circular functions because they are about the unit circle. We call them trigonometric functions.

    sec(theta) = -sqrt(2)
    (I guess you are not allowed to use calulators yet.)
    sec = hyp/adj

    Oh, in the unit circle, in the reference right triangle for angle theta,
    opposite side, or opp, is the vertical side opposite angle theta
    adjacent side, or adj, is the horizontal side adjacent to angle theta
    hypotenuse, or hyp, is the hypotenuse of the reference right triangle.
    (hyp)^2 = (opp)^2 +(adj)^2

    So, hyp = sqrt(2), .......hypotenuse is always positive.
    and adj = -1
    Therefore, opp = sqrt[(-sqrt(2))^2 -(1)^2]
    opp = sqrt[2 -1] = sqrt[1] = 1

    So for angle theta,
    opp = 1
    adj = -1
    hyp = sqrt(2)
    theta then is basically 45 degrees
    Since adj is negative, it means theta is either in the 2nd or 3rd quadrants because the adjacent side of the reference triangle lies on the negative side of the horizontal axis or x-axis.

    So, in the 2nd quadrant, theta = 180 -45 = 135 degrees, and/or,
    in the 3rd quadrant, theta = 180 +45 = 225 degrees -------answer.

    -----------------------------------------
    cot theta = infinity

    Meaning, since cot = adj/opp,
    adj = +,-1
    opp = 0

    Since opp is vertical, theta then has no vertical side.
    Theta lies on the x-axis.
    Theta then is either 0 degree or 180 degrees. ------answer.
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