Results 1 to 3 of 3

Math Help - Trig Crazy

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    14

    Trig Crazy

    Evaluate:
    a) tan(cos^-1(1/3)

    b) Solve the pair of equations cosx=-1/2 and tanx=root3 for 0<-x<-2pi
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,553
    Thanks
    542
    Hello, redpanda11!

    a) Evaluate: . \tan\left[\cos^{-1}\!\left(\frac{1}{3}\right)\right]
    Recall that an inverse trig function is an angle.

    Let: \theta = \cos^{-1}\!\left(\frac{1}{3}\right)\quad\Rightarrow\quad\  cos\theta \:=\:\frac{1}{3} \:=\:\frac{adj}{hyp}

    \theta is in a right triangle with: adj = 1,\:hyp = 3
    Using Pythagorus, we find that: . opp \:= \:\sqrt{8} \:=\:2\sqrt{2}
    Then: . \tan\theta \:=\:\frac{opp}{adj} \:=\:\frac{2\sqrt{2}}{1} \:=\:2\sqrt{2}\quad\Rightarrow\quad \theta \:=\:\tan^{-1}\left(2\sqrt{2}\right)<br />

    Therefore, we have: . \tan\left[\tan^{-1}\!\left(2\sqrt{2}\right)\right] \;=\;\boxed{2\sqrt{2}}



    b) Solve the pair of equations: \cos x = \text{-}\frac{1}{2} and \tan x = \sqrt{3} . for 0 \leq x \leq 2\pi

    Cosine is negative in Quadrants 2 and 3.
    Tangent is positive in Quadrants 1 and 3.
    . . Hence, x is in Quadrant 3.

    Multiply the two equations: . (\cos x)(\tan x) \;=\;\left(-\frac{1}{2}\right)\left(\sqrt{3}\right)

    Then we have: . \cos x\cdot\frac{\sin x}{\cos x} \;=\;-\frac{\sqrt{3}}{2}\quad\Rightarrow\quad\sin x \:=\:-\frac{\sqrt{3}}{2}

    Therefore: . \boxed{x \;=\;\frac{4\pi}{3}}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Ooh multiplying equations... never thought of it, but it does make sense
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Crazy puzzle
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 30th 2010, 01:44 PM
  2. Going crazy on this log question!
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 16th 2009, 05:35 AM
  3. Crazy integral
    Posted in the Math Challenge Problems Forum
    Replies: 4
    Last Post: July 10th 2009, 02:51 AM
  4. crazy limit
    Posted in the Calculus Forum
    Replies: 22
    Last Post: June 13th 2008, 08:00 AM
  5. I am going crazy, please help!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 22nd 2006, 07:15 AM

Search Tags


/mathhelpforum @mathhelpforum