Results 1 to 11 of 11

Math Help - Finding all solutions to Trig Equations

  1. #1
    Junior Member
    Joined
    Jul 2010
    Posts
    55

    Finding all solutions to Trig Equations

    I'm working on a few problems where I have to figure out all solutions to a given equation between [0,2PI). Here's one i got but i'm not all that sure that it is correct:




    tan x ^ 2 - 2 tan x - 3 = 0


    My Solution:

    (tan x - 3) (tan x + 1) = 0

    tan x = 3 , tan x = -1


    Both have no solution.

    I don't think this is right though, i've yet to solve any of these problems where i didn't find at least one solution. I'm guessing i would probably have to solve it another way correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    3pi/4 is a solution to tan(x) = -1.
    Last edited by mr fantastic; April 18th 2011 at 01:42 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    611
    Hello, MajorJohnson!

    Find all solutions on [0, 2pi]

    . . (tan x)^2 - 2(tan x) - 3 .= .0


    My Solution:

    . . (tan x - 3)(tan x + 1) .= .0

    . . tan x =3 . . . tan x = -1

    Both have no solution. . What?

    Did you try your calculator?

    . . x .= .arctan(3) . .0.40(pi)

    . . x .= .arctan(-1) .= .0.75(pi)

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jul 2010
    Posts
    55
    I don't seem to get those solutions when i enter in arctan.


    I see where you get 3PI/4 from tangent and i think 7PI / 4 would be the next one.

    As for 3 i'm not sure.
    Last edited by MajorJohnson; April 16th 2011 at 02:51 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by MajorJohnson View Post
    I don't seem to get those solutions when i enter in arctan.


    I see where you get 3PI/4 from tangent and i think 7PI / 4 would be the next one.

    As for 3 i'm not sure.
    Two comments....first is your calculator in degree or radian mode? Also Soroban is giving his answers in terms of multiples of pi. To get his answer for atan(-1), for example, plug in atan(-1) to get -0.785398, then divide by pi = 3.1415927. You will get -0.25. I'll let you figure out how Soroban got 0.75. (Hint: Think about what quadrant the angle -1 rad is in.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jul 2010
    Posts
    55
    Question: Why did you divide by PI?

    I was able to get that answer by doing what you described above.

    Tan 3 is in quadrant 1 and 3.


    so plugging in Tan (3) will give me -.14254... and i'll divide that by PI to give me -.04537...
    Last edited by MajorJohnson; April 18th 2011 at 05:27 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by MajorJohnson View Post
    I was able to get that answer by doing what you described above.

    Next i have to find the decimal of each radian. For finding the decimal of a csc, sec, and cot i type on my calculator 1/sin(PI/6) right?
    That's csc(pi/6), yes. then sec() = 1/cos() and cot() = 1/tan().

    -Dan
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jul 2010
    Posts
    55
    So following your previous post:

    Why did you divide by PI?

    Tan 3 would be in in quadrant 1 and 3.

    so plugging in Tan (3) will give me -.14254... and i'll divide that by PI to give me -.04537...

    But i still think that tan 3 would be present no solution because it is greater than 1. So the answer in radians would just be
    3PI/4 and 7PI/4 right?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by MajorJohnson View Post
    So following your previous post:

    Why did you divide by PI?

    Tan 3 would be in in quadrant 1 and 3.

    so plugging in Tan (3) will give me -.14254... and i'll divide that by PI to give me -.04537...

    But i still think that tan 3 would be present no solution because it is greater than 1. So the answer in radians would just be
    3PI/4 and 7PI/4 right?
    tan(x) can be any real number. You are confusing the range of tan with the range of sine and cosine.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Jul 2010
    Posts
    55
    okay, so if 3 is acceptable, how would i find the radian measure on a 360 degree circle, i haven't learned how to solve it for this specific number only for ones up to 1.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by MajorJohnson View Post
    okay, so if 3 is acceptable, how would i find the radian measure on a 360 degree circle, i haven't learned how to solve it for this specific number only for ones up to 1.
    Posts # 2 and #3 gave you most of the answer. Below are all the solutions. You need to become more familiar with the symmetry of the unit circle, as well as the tan function. I suggest you thoroughly revise that material.

    Quote Originally Posted by e^(i*pi) View Post
    3pi/4 is a solution to tan(x) = -1.
    7 pi/4 is another.

    And the solution to tan(x) = 3 is x = arctan(3) or x = pi + arctan(3).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding Exact Solutions Trig Equations
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: December 11th 2011, 04:42 PM
  2. Finding all solutions to the trig equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 11th 2010, 10:00 PM
  3. Solutions to trig equations
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: August 10th 2010, 05:30 AM
  4. finding solutions in trig
    Posted in the Trigonometry Forum
    Replies: 17
    Last Post: June 30th 2008, 08:06 PM
  5. Trig question finding all solutions
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 27th 2006, 04:52 PM

Search Tags


/mathhelpforum @mathhelpforum