Results 1 to 3 of 3

Thread: What's the difference between these two trig identity problems?

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    175

    What's the difference between these two trig identity problems?

    1) $\displaystyle 2 \tan x=3 \sin x$
    $\displaystyle 2 \frac{\sin x}{\cos x}=3 \sin x \rightarrow$ $\displaystyle 2 \sin x = 3 \sin x \cos x \rightarrow$ $\displaystyle \sin x(2 - 3 \cos x)=0$
    a) $\displaystyle \sin x = 0 \rightarrow x =180n$
    b) $\displaystyle \cos x = \frac{2}{3} \rightarrow x =$48.19 + 360n

    2) $\displaystyle 2 \sin 2x \cos ^2 x = \sin 2x$
    $\displaystyle \sin 2x(2 \cos ^2 x -1) =0 \rightarrow$
    a) $\displaystyle \sin 2x=0 \rightarrow 2x=180n \rightarrow x = 90n$
    b) $\displaystyle \cos ^2 x = \frac{1}{2} \rightarrow \cos x = \pm \sqrt{\frac{1}{2} }$
    $\displaystyle x = \pm$ 45 + 360n

    of course the answer to number 2 is $\displaystyle \pm$ 45 + 180n
    but the answer to number 1 is 48.19 + 360n! So what's the difference between the two? They are both cosine functions. I just thought always add 360 degrees because that's when the angle repeats itself.

    (*fixed the bold...)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Pim
    Pim is offline
    Member
    Joined
    Dec 2008
    From
    The Netherlands
    Posts
    91
    $\displaystyle \cos x = \pm \frac{1}{2}\sqrt{2}$ has four solutions on $\displaystyle [0,360]$
    These are 45, 135, 225 and 315
    45 + 360n and 135 + 360n can be rewritten as 45+180n, because they are half a period apart.
    Same goes for 135 and 315 (where -45 is 315-360)
    You could sum up all solutions as 45+90n

    Do you understand now?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    Posts
    175
    touche
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum/Difference Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Nov 15th 2009, 07:48 AM
  2. Proving Trig Identity: Sine Difference
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Sep 4th 2009, 04:02 AM
  3. Trig Identity Problems
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Nov 29th 2008, 10:26 AM
  4. Sum and Difference Identity question
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 7th 2008, 07:10 AM
  5. Simplish trig identity problems
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Nov 9th 2007, 01:10 PM

Search Tags


/mathhelpforum @mathhelpforum