Results 1 to 5 of 5

Math Help - Trig without using a calculator help

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    23

    Trig without using a calculator help

    Really struggling with this one.

    Given that Θ is an acute angle and that tanΘ=8/9 find, without using a calculator the value of sin 2

    Can anyone shed some light on how it is done
    Many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,516
    Thanks
    1404
    Quote Originally Posted by jamm89 View Post
    Really struggling with this one.

    Given that Θ is an acute angle and that tanΘ=8/9 find, without using a calculator the value of sin 2

    Can anyone shed some light on how it is done
    Many thanks
    I think you need to double check that you've written the question right. ATM it doesn't make any sense.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member sinewave85's Avatar
    Joined
    Oct 2006
    From
    Lost in a series of tubes.
    Posts
    218
    Quote Originally Posted by jamm89 View Post
    Really struggling with this one.

    Given that Θ is an acute angle and that tanΘ=8/9 find, without using a calculator the value of sin 2

    Can anyone shed some light on how it is done
    Many thanks
    Ok, the basic principle here is that tanΘ = sinΘ/cosΘ, so sinΘ = 8/h and cosΘ = 9/h. That said, the value of the sin 2 is the value of the sin 2, which is not dependent on what you introduced the problem with. Are you sure you typed it out exactly as is written in the book? Is it not sin(2Θ)?
    Last edited by sinewave85; March 5th 2009 at 01:01 PM. Reason: oops -- typos: sinΘ = 8/h, cosΘ = 9/h
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2009
    Posts
    23
    Quote Originally Posted by sinewave85 View Post
    Ok, the basic principle here is that tanΘ = sinΘ/cosΘ, so sinΘ = 8 and cosΘ = 9. That said, the sin2 is sin2, which is not dependent on what you introduced the problem with. Are you sure you typed it out exactly as is written in the book? Is it not sin(2Θ)?
    Sorry guys it is sin(2Θ)

    That makes more sense now lol
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,714
    Thanks
    633
    Hello, jamm89!

    We need this identity: . \sin2\theta \:=\:2\sin\theta\cos\theta


    Given that \theta is an acute angle and that \tan\theta = \tfrac{8}{9}
    find, without using a calculator the value of: \sin 2\theta

    We are given: . \tan\theta \:=\:\frac{8}{9} \:=\:\frac{opp}{adj}

    So \theta is an acute angle in a right triangle with: . opp = 8,\:adj = 9

    Using Pythagorus, we find that: . hyp \:=\:\sqrt{145}

    . . Then: . \begin{array}{c}\sin\theta \:=\:\frac{opp}{hyp} \:=\:\frac{8}{\sqrt{145}} \\ \\[-3mm]\cos\theta \:=\:\frac{adj}{hyp} \:=\:\frac{9}{\sqrt{145}} \end{array}


    Therefore: . \sin2\theta \;=\;2\sin\theta\cos\theta \;=\;2\left(\frac{8}{\sqrt{145}}\right)\left(\frac  {9}{\sqrt{145}}\right) \;=\;\boxed{\frac{144}{145}}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 6th 2012, 02:16 PM
  2. Replies: 4
    Last Post: April 20th 2011, 05:33 AM
  3. Trig ratio as fraction on calculator
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 15th 2011, 08:12 AM
  4. calculating trig. ratios w/ out a calculator
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: April 12th 2011, 06:35 PM
  5. trig functions on a calculator
    Posted in the Calculators Forum
    Replies: 1
    Last Post: April 28th 2010, 09:56 AM

Search Tags


/mathhelpforum @mathhelpforum