Results 1 to 2 of 2

Math Help - solving trig equations (in radians)

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    60

    solving trig equations (in radians)

    Solve for 0 < Θ < 2pi
    1. 2secΘ + 9 = 5cosΘ

    Solve for the same, but without using a calculator.
    1. root3tan^2Θ + tanΘ = 0

    please help? thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,110
    Thanks
    382
    Awards
    1
    Quote Originally Posted by checkmarks View Post
    Solve for 0 < Θ < 2pi
    1. 2secΘ + 9 = 5cosΘ
    Call t = theta for convenience.

    sec(t) = 1/cos(t), so
    2/cos(t) + 9 = 5cos(t) <-- Multiply both sides by cos(t):

    2 + 9cos(t) = 5cos^2(t)

    5cos^2(t) - 9cos(t) - 2 = 0

    Let x = cos(t)

    5x^2 - 9x - 2 = 0

    (5x + 1)(x - 2) = 0

    x = -1/5 or x = 2

    Thus
    cos(t) = -1/5 or cos(t) = 2 <-- Impossible

    Thus
    cos(t) = -1/5

    Thus
    t = acs(-1/5) = 1.772 rad = 0.5641(pi)

    Now, this angle is slightly larger than (pi)/2, so it is in quadrant II. The reference angle is (pi) - 0.5641(pi) = 0.4359(pi). There is another such angle where cosine is negative: Quadrant III. So the other angle will be (pi) + 0.4359(pi) = 1.4360(pi). Thus your answers are:

    t = 0.5641(pi) or t = 1.4360(pi)

    -Dan
    [/quote]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving trig equations
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 4th 2010, 02:23 PM
  2. solving trig equations
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 14th 2008, 05:03 PM
  3. Help with solving trig equations
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 1st 2007, 06:47 AM
  4. Solving Trig Equations
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: November 25th 2007, 06:27 AM
  5. Solving Trig Equations
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 21st 2007, 07:18 PM

Search Tags


/mathhelpforum @mathhelpforum