Results 1 to 7 of 7

Math Help - How do I find cos[arctan(3/5)] ?

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    23

    How do I find cos[arctan(3/5)] ?

    How do i find cos[arctan(3/5)] ?

    I know I need to set up some kind of triangle diagram, but I don't know how or what to do next. I am not allowed to use a calculator.

    Thanks to anyone that tries to help me.

    --Cori
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by liz155 View Post
    How do i find cos[arctan(3/5)] ?

    I know I need to set up some kind of triangle diagram, but I don't know how or what to do next. I am not allowed to use a calculator.

    Thanks to anyone that tries to help me.

    --Cori
    Let \arctan \left( \frac {3}{5} \right) = \theta \implies \tan \theta = \frac {3}{5}

    Thus we can set up a right-triangle and label one of the acute angles "theta" and fill in the sides accordingly. (tangent = opposite/adjacent). we can use Pythagoras' theorem to find the length of the hypotenuse, which here is \sqrt {34}

    Thus we can say, \cos \left[ \arctan \left( \frac {3}{5} \right) \right] = \cos \theta = ?

    It shouldn't be too hard for you to finish, right?
    Attached Thumbnails Attached Thumbnails How do I find cos[arctan(3/5)] ?-tri2.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2007
    Posts
    23
    Since cos= adjacent over hypotenuse...Would the answer be 5/sqrt(34)?

    Thanks so much for your help and the great picture!!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by liz155 View Post
    Since cos= adjacent over hypotenuse...Would the answer be 5/sqrt(34)?

    Thanks so much for your help and the great picture!!!
    correct
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2007
    Posts
    23
    Thanks again! I really understand it now.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by liz155 View Post
    Thanks again! I really understand it now.
    you're welcome.

    note the technique, it works on a lot of problems of this nature. with some their are alternatives though, you can use trig identities to work them out, but let's save those for another time
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    12
    Quote Originally Posted by liz155 View Post
    How do i find cos[arctan(3/5)] ?
    Also, you can try to prove that \cos x=\frac1{\sqrt{1+\tan^2x}}\implies\cos(\arctan x)=\frac1{\sqrt{1+x^2}}

    Plugging x=\frac35 you have the asked.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the value of cot^-1 given arctan
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 18th 2011, 03:25 PM
  2. arctan(y) = x^2 + C, y = ?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 17th 2010, 03:39 AM
  3. find the derivative with arctan
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 31st 2010, 02:03 PM
  4. FInd exact value of the expression Sec(arctan -5/12)
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: July 1st 2008, 02:45 AM
  5. arctan(x)
    Posted in the LaTeX Help Forum
    Replies: 6
    Last Post: June 2nd 2008, 08:51 PM

Search Tags


/mathhelpforum @mathhelpforum