Results 1 to 7 of 7

Math Help - Trigonometric Equation help need!

  1. #1
    nee
    nee is offline
    Junior Member
    Joined
    Aug 2008
    Posts
    36

    Trigonometric Equation help need!

    Solve the equation for solutions over the interval [0, 360).

    sec(squared)xtanx = 2tanx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    nee
    nee is offline
    Junior Member
    Joined
    Aug 2008
    Posts
    36
    Ok I think I got it:

    sec(squared)xtanx = 2tanx

    sec(squared)xtanx - 2tanx = 0

    sec(squared)xtanx - tanx - tanx = 0

    tanx(sec(squared)x - 2) = 0

    tanx = 0 or sec(squared)x - 2 = 0
    sec(squared)x = 2
    secx = (squareroot)2

    therefore:
    a(squared) + b(squared) = c(squared)
    1(squared) + b(squared) = ((squareroot)2)(squared)
    1 + b(squared) = 2
    1 + 1 = 2 (if I'm not mistaken)

    therefore tanx = + or - 1

    therefore solution set:
    {0. 45, 135, 180, 225, 315)

    correct me if me wrong please

    NEE!!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    From
    Georgia
    Posts
    85
    Quote Originally Posted by nee View Post
    Ok I think I got it:

    sec(squared)xtanx = 2tanx

    sec(squared)xtanx - 2tanx = 0

    sec(squared)xtanx - tanx - tanx = 0

    tanx(sec(squared)x - 2) = 0

    tanx = 0 or sec(squared)x - 2 = 0
    sec(squared)x = 2
    secx = (squareroot)2

    therefore:
    a(squared) + b(squared) = c(squared)
    1(squared) + b(squared) = ((squareroot)2)(squared)
    1 + b(squared) = 2
    1 + 1 = 2 (if I'm not mistaken)

    therefore tanx = + or - 1

    therefore solution set:
    {0. 45, 135, 180, 225, 315)

    correct me if me wrong please

    NEE!!
    The 1+b^2=\sqrt{2}, i dunno where you got that from. It's not needed or necessary to solve this equation.

    You got it right up to that point. Which angles does tan x = 0 and where does sec x = \frac{1}{\sqrt{2}}, which is actually cos x = \frac{\sqrt{2}}{2}, fall on? Find the angles, and you'll have your solution.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    nee
    nee is offline
    Junior Member
    Joined
    Aug 2008
    Posts
    36
    Gotcha, that does make more sense. Thanks, NEE!!!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    \sec^2x \tan x=2 \tan x

    \sec^2x=2

    \frac{1}{\cos^2x}=2

    2\cos^2x=1

    \cos^2x=\frac{1}{2}

    \cos x=\frac{\sqrt{2}}{2}

    x=\frac{\pi}{4} \ \ or \ \ \frac{7\pi}{4}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hi,
    Quote Originally Posted by masters View Post
    \sec^2x \tan x=2 \tan x

    \sec^2x=2

    \frac{1}{\cos^2x}=2

    2\cos^2x=1

    \cos^2x=\frac{1}{2}

    \cos x=\frac{\sqrt{2}}{2}

    x=\frac{\pi}{4} \ \ or \ \ \frac{7\pi}{4}
    Consider the solution \tan(x)=0
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Moo View Post
    Hi,

    Consider the solution \tan(x)=0
    Ok, then we have {0, \frac{\pi}{4}, \pi, \frac{7\pi}{4}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 27th 2011, 01:26 AM
  2. trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: September 9th 2009, 07:36 AM
  3. trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 22nd 2009, 01:59 AM
  4. Replies: 2
    Last Post: April 28th 2009, 07:42 AM
  5. Trigonometric Equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 5th 2008, 11:19 AM

Search Tags


/mathhelpforum @mathhelpforum