Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Soroban

Math Help - Trig Ratios

  1. #1
    Member
    Joined
    Sep 2012
    From
    US
    Posts
    123

    Trig Ratios

    Find the remaining trigonometric ratios.

    tan (a) = 4, 0<a<pi/2


    sin(α)
    =
    cos(α)
    =
    cot(α)
    =
    sec(α)
    =
    csc(α)
    =
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Trig Ratios

    I would use the Pythagorean identities, keeping in mind all roots will be positive since the angle given is in the first quadrant. For example:

    \tan(a)=4

    \frac{\sin(a)}{\cos(a)}=4

    \sin(a)=4\cos(a)

    \sin^2(a)=16\cos^2(a)

    \sin^2(a)=16(1-\sin^2(a))

    17\sin^2(a)=16

    \sin^2(a)=\frac{16}{17}

    \sin(a)=\frac{4}{\sqrt{17}}

    You can now easily find \cos(a) from \sin(a)=4\cos(a). Now that you have the three primary functions, finding the rest is straightforward...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2012
    From
    US
    Posts
    123

    Re: Trig Ratios

    So would cos(a) be the same as sin (a), and the rest would be just reciprocals? Sorry I haven't done this in a long time :S
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Trig Ratios

    No, from the equation relating sin(a) and cos(a), we see that cos(a) is 1/4 the value of sin(a). Then yes, the secondary functions would be the reciprocals of the corresponding primary functions.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    769

    Re: Trig Ratios

    Hello, Oldspice1212!

    Given: . \tan\theta \,=\,4,\;0 < \theta < \tfrac{\pi}{2}
    Find the remaining trigonometric ratios.

    We are given: . \tan\theta\:=\:\frac{4}{1}\:=\:\frac{opp}{adj}

    \theta is in a right triangle with: opp = 4,\:adj = 1
    Pythagorus tells us that: hyp \:=\:\sqrt{4^2+1^2} \:=\:\sqrt{17}

    So we have: . \begin{Bmatrix}opp &=& 4 \\ adj &=& 1 \\ hyp &=& \sqrt{17} \end{Bmatrix}


    And we can write all six trig ratios:

    . . \begin{array}{cccccccccc}\sin\theta &=& \frac{4}{\sqrt{17}} &\;\;& \csc\theta &=& \frac{\sqrt{17}}{4} \\ \\[-3mm] \cos\theta &=& \frac{1}{\sqrt{17}} && \sec\theta &=& \sqrt{17} \\ \\[-3mm] \tan\theta &=& 4 && \cot\theta &=& \frac{1}{4} \end{array}
    Thanks from MarkFL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig ratios
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 27th 2011, 01:42 AM
  2. ratios and trig ratios
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 7th 2011, 10:45 AM
  3. Trig. ratios and trig expressions
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 22nd 2010, 10:58 AM
  4. trig ratios
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 3rd 2010, 07:24 AM
  5. Replies: 6
    Last Post: November 20th 2009, 05:27 PM

Search Tags


/mathhelpforum @mathhelpforum