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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: droodles on December 03, 2007, 10:36:01 pm

Title: solve for the following equation
Post by: droodles on December 03, 2007, 10:36:01 pm: (http://img99.imageshack.us/img99/3259/27176368le8.png) DOMAIN x [0,2]

sin (2∏x)=-1/2
-sin (2∏x) = ∏/6

???
Title: Re: solve for the following equation
Post by: Collin Li on December 03, 2007, 10:41:44 pm: 2sin(2pix) = -1, dom: [0,2]

period = 2pi/2pi = 1

=> sin(2pix) = -1/2

Negative solution: Q3 and Q4
=> 2pix = 7pi/6, 11pi/6
=> x = 7/12, 11/12

Add/subtract periods to get all solutions for x from [0,2]:
x = 7/12, 11/12, 19/12, 23/12
Title: Re: solve for the following equation
Post by: Neobeo on December 03, 2007, 10:51:05 pm: LaTeX test. Also, wondering if it was possible to insert a linebreak.

Solve for x in the domain [0,2]:

$2sin(2\pi x)=-1$

Solution by coblin:

$2sin(2\pi x)=-1$ , dom: $[0,2]$

Period = $\frac{2\pi}{2\pi}=1$
$\Rightarrow sin(2\pi x)=-\frac{1}{2}$

Negative solution: Q3 and Q4
$\Rightarrow 2\pi x=\frac{7\pi}{6},\frac{11\pi}{6}$
$\Rightarrow x=\frac{7}{12},\frac{11}{12}$

Add/subtract periods to get all solutions for x from [0,2]:
$x=\frac{7}{12},\frac{11}{12},\frac{19}{12},\frac{23}{12}$
Title: Re: solve for the following equation
Post by: Ahmad on December 04, 2007, 04:34:52 pm: Neobeo, using \sin rather than just sin is preferred when using $\LaTeX$ :)

Compare:
$\sin (x)$ rather than $sin(x)$