Results 1 to 4 of 4

Math Help - Cos/Sin Problems

  1. #1
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Cos/Sin Problems

    None of the Problems can contain a Trig Identity...

    cos(t)=-5/6

    pi<t< 3pi/t

    Give exact answers, do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2).

    Unknowns:

    Sin(2t)=?
    Cos(t/2)=?
    sin(t/2)=?
    Last edited by qbkr21; November 20th 2006 at 04:15 PM. Reason: I wanted to add something...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630
    Hello, qbkr21!

    Given: . \cos(t) = -\frac{5}{6},\;\;\pi < t < \frac{3\pi}{2}

    Find: . (a)\;\sin(2t)\qquad(b)\;\cos\left(\frac{t}{2}\righ  t)\qquad(c)\;\sin\left(\frac{t}{2}\right)

    We are told that: . \cos(t) \:=\:-\frac{5}{6}

    Since \cos(t) \,=\,\frac{adj}{hyp}, we know that: . adj = -5,\;hyp = 6

    Pythagorus says: . (opp)^2 + (adj)^2 \:=\:(hyp)^2
    . . so we have: . (opp)^2 + (-5)^2 \:=\:6^2\quad\Rightarrow\quad(opp)^2 \:=\:11\quad\Rightarrow\quad opp = \pm\sqrt{11}

    Since t is in quadrant 3, opp = -\sqrt{11}

    So we have: . \sin(t) \:=\:-\frac{\sqrt{11}}{6}\qquad \cos(t) \:=\:-\frac{5}{6}

    Now with a few identities, we can tackle the questions . . .


    (a)\;\sin(2t) \:=\:2\sin(t)\cos(t) \:=\:2\left(-\frac{\sqrt{11}}{6}\right)\left(-\frac{5}{6}\right) \:=\:\frac{5\sqrt{11}}{18}


    (b)\;\cos\left(\frac{t}{2}\right) \:=\:\pm\sqrt{\frac{1 + \cos t}{2}} \:= \:\pm\sqrt{\frac{1 - \left(-\frac{5}{6}\right)}{2}} \:=\:\pm\sqrt{\frac{1}{12}} \:=\:\pm\frac{\sqrt{3}}{6}

    . . .Since t is in quadrant 3, \frac{t}{2} is in quadrant 2 where cosine is negative.

    . . .Therefore: . \cos\left(\frac{t}{2}\right)\;=\;-\frac{\sqrt{3}}{6}


    (c)\;\sin\left(\frac{t}{2}\right) \:=\:\pm\sqrt{\frac{1-\cos(t)}{2}} \:=\:\pm\sqrt{\frac{1-\left(-\frac{5}{6}\right)}{2}} \:=\:\pm\sqrt{\frac{11}{12}}\:=\:\pm\frac{\sqrt{33  }}{6}

    . . .Since t is in quadrant 3, \frac{t}{2} is in quadrant 2 where sine is positive.

    . . .Therefore: . \sin\left(\frac{t}{2}\right) \;=\;\frac{\sqrt{33}}{6}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    RE:Thanks so Much!!

    Thanks Soroban you guys are such brains...really am baffeled by how much you guys know, no one needs to know this much math, this is all crazy!!!


    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Dude I don't think you realize how much easier you have made this for me. I have but in 20 plus hours over the past 2 days, and for the first time since reading you post this is now clicking. Gosh I really, really thank you for help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 3rd 2011, 05:35 AM
  2. binomial problems/normal problems
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 19th 2010, 11:46 PM
  3. binomial problems as normal problems
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 19th 2010, 11:41 PM
  4. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 05:39 PM
  5. 2 Problems, need help, story problems!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 23rd 2007, 10:43 PM

Search Tags


/mathhelpforum @mathhelpforum