Results 1 to 3 of 3

Math Help - Simple Trigonometry help, and logs

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    64

    Simple Trigonometry help, and logs

    How would i go about working out:

    1. cos(x) + sin(x) = (1/3), -pi < x < pi

    2. ln(y+1) - ln(y) = 0.85
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    For the first one, I'd make a substitution with u=cos(x).

    As cos²(x)+sin²(x)=1, sin(x)=sqrt(1-cos²(x))=sqrt(1-u²)

    Thus we have u+\sqrt{1-u^2}=1/3

    1/3-u=\sqrt{1-u^2}

    Square the whole equation and solve for u, then deduct the values for x.



    For the second one : \ln(a)-\ln(b)=\ln(\frac ab)
    So it's equivalent to :

    \frac{y+1}{y}=e^{0.85}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, Stylis10!


    Another approach to #1 . . .


    1.\;\;\cos x + \sin x \:=\:\frac{1}{3}\qquad -\pi < x < \pi
    Divide by \sqrt{2}\!:\qquad \frac{1}{\sqrt{2}}\cos x + \frac{1}{\sqrt{2}}\sin x \:=\:\frac{1}{3\sqrt{2}}

    And we have: . \sin\frac{\pi}{4}\cos x + \cos\frac{\pi}{4}\sin x \:=\:\frac{\sqrt{2}}{6}

    . . . . . . . . . . . . . . . . . \sin\left(\frac{\pi}{4}+x\right) \:=\:\frac{\sqrt{2}}{6}


    Hence: . \frac{\pi}{4}+x \:=\:\sin^{-1}\left(\frac{\sqrt{2}}{6}\right) \quad\Rightarrow\quad x \;=\;\sin^{-1}\left(\frac{\sqrt{2}}{6}\right) - \frac{\pi}{4}


    . . Therefore: . x \;=\;\begin{Bmatrix}\text{-}0.547457039 \\ \;2.118253365 \end{Bmatrix}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simple logs
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 9th 2010, 10:30 PM
  2. simple logs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 6th 2010, 02:02 AM
  3. Pretty simple trigonometry but need help
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 20th 2010, 12:25 PM
  4. trigonometry and logs
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 1st 2009, 09:33 AM
  5. Simple Trigonometry Help
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: January 25th 2009, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum