Results 1 to 3 of 3

Math Help - Inverse Trig

  1. #1
    Junior Member
    Joined
    Dec 2007
    Posts
    32

    Inverse Trig

    The problem is

    Determine the exact value of

    sin (2 arccos (8/17))

    The triangle for sin (arccos x) = sqroot(1-x^2). I have no idea how the answer is (240/289).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,751
    Thanks
    651
    Hello, shogunhd!

    Determine the exact value of: . \sin\left[2\arccos\left(\frac{8}{17}\right)\right]

    Let \theta \:=\:\arccos\left(\frac{8}{17}\right)\quad\Rightar  row\quad\cos\theta \:=\:\frac{8}{17} \:=\:\frac{adj}{hyp}

    So, \theta is in a right triangle with: .  adj = 8,\;hyp = 17
    . . Using Pythagorus, we find that: . opp = 15
    Hence: . \sin\theta = \frac{15}{17},\;\cos\theta = \frac{8}{17}

    The problem becomes: . \sin(2\theta) \;=\;2\sin\theta\cos\theta \:=\:2\left(\frac{15}{17}\right)\left(\frac{8}{17}  \right) \;=\;\frac{240}{289}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by shogunhd View Post
    Determine the exact value of

    sin (2 arccos (8/17))
    Similar to this problem.

    Since \sin (\arccos \varphi ) = \sqrt {1 - \varphi ^2 } \implies \sin (2\arccos \varphi ) = 2\varphi \sqrt {1 - \varphi ^2 } .

    Plug \varphi=\frac8{17} and you're done.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverse Trig
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 19th 2011, 01:19 PM
  2. Find the value of 'trig of inverse trig' questions
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 9th 2010, 05:37 PM
  3. inverse trig?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 21st 2010, 02:01 PM
  4. inverse trig values and finding inverse
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 6th 2009, 12:04 AM
  5. Inverse Trig Functions and Advance Trig
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 24th 2008, 03:13 PM

Search Tags


/mathhelpforum @mathhelpforum