Results 1 to 4 of 4

Math Help - Trig

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    20

    Trig

    Solve the equation 1 - 3cos^2 x = -5sinx for x in the range 0<(or equal) x <(or equal) to 2pi. Where x is correct to 3 decimal places.

    thankkks !
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2008
    Posts
    1

    trig

    1-3cos^2x = -5sin x
    -3cos^x + 5sin x +1 = 0
    -3(1-sin^2 x) + 5sin x +1 = 0
    3sin^2 x + 5sin x -2 = 0
    then x = sin x
    replace sine with x so it will give you a quadratic equation.

    3x^2 + 5 x -2=0

    solutions are

    x = -2/3 and x = -1
    then your x was sine, so
    sinx = -2/3 , sinx = -1
    then if 0<(or =)x<(or=) 2pi
    x=5.665 x = 4.712
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    7

    Smile

    first, cos^2x = 1- sin^2X.
    then we get 1-3(1-sin^2x)=-5sinx
    so, 3sin^2x+5sinx-2=0
    (sinx+2)(3sinx-1)=0 --> sinx=-2 or sinx=1/3
    however, sinx has to stay in range -1 to 1, therefore sinx can't be -2
    then, sinx=1/3 -->using calculator we get, arcsin(1/3)=0.3398369095...
    thus answer is 0.340 (to 3 decimal places)
    and the another one is pi-0.3398369095=2.802 (in 4th quard)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2008
    Posts
    7
    Quote Originally Posted by anki View Post
    1-3cos^2x = -5sin x
    -3cos^x + 5sin x +1 = 0
    -3(1-sin^2 x) + 5sin x +1 = 0
    3sin^2 x + 5sin x -2 = 0
    then x = sin x
    replace sine with x so it will give you a quadratic equation.

    3x^2 + 5 x -2=0

    solutions are

    x = -2/3 and x = -1
    then your x was sine, so
    sinx = -2/3 , sinx = -1
    then if 0<(or =)x<(or=) 2pi
    x=5.665 x = 4.712
    x = -2/3 and x = -1 ????????????
    try to plug in with x=-1, what'd you get? 3-5-2=-4
    Last edited by CaptainBlack; November 4th 2008 at 11:55 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Compute Trig Function Values, Solve Trig Equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 8th 2011, 08:00 PM
  2. Replies: 7
    Last Post: April 15th 2010, 09:12 PM
  3. Replies: 6
    Last Post: November 20th 2009, 05:27 PM
  4. Replies: 1
    Last Post: July 24th 2009, 03:29 AM
  5. Trig Equations with Multiple Trig Functions cont.
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 7th 2008, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum