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2006 paper 1 question 7 - HSN forum

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2006 paper 1 question 7


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#1 Amazoph

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Posted 14 May 2007 - 08:34 PM

I'm completely stuck on this question... goes as follows:

Solve the equation  sin x - sin 2x = 0 in the interval 0 < x < 360

I don't know where to go from here.. expanding the sin2x just makes it even more complicated :/

#2 Gillz

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Posted 14 May 2007 - 08:53 PM

sinx - sin2x = 0

sinx - 2sinxcosx = 0

sinx (1 - 2cosx) = 0

sinx = 0 , 1 - 2cosx = 0
1 = 2cosx
1/2 = cosx
cos-1 (1/2) = x
60 = x


then for sinx => 0
180 - 0 = 180
360
cosx => 60
360 - 60 = 300

hence, x = 0, 180, 360, 60, 300

not very well explained unfortunately, hopefully you get the idea though smile.gif .

#3 babeasc

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Posted 14 May 2007 - 08:53 PM



\begin{align*}\sin x - \sin (2x) &= 0 \\ \sin x - 1 - 2\sin ^2 x &=0 \\ -2\sin ^2 x + \sin x - 1 &=0\end{align*}

compare this witht the form



\begin{align*}ax^2 + bx + c &= 0 \\ -2x^2 +x -1 &=0 \\ (2x-1)(x+1) &=0\end{align*}

return to original format



\begin{align*}(2\sin x - 1)(\sin x +1) &=0 \\\end{align*}

either


\begin{align*}2 \sin x - 1 &= 0 \\ 2 \sin x &=1 \\ \sin x &= \frac{1}{2} \\ x &= \sin ^{-1} \frac{1}{2} \\ x &= 30; 150 (180-30)\end{align*}

or


\begin{align*} \sin x + 1 &= 0 \\  \sin x &= -1 \\ x &= \sin ^{-1} -1\\ x &= 270\end{align*}

so, x = 30, 150, 270; 0<x<360



Beyond it, and us, shines a greater hope and a brighter future
Can't wait 'til the exams are over!

#4 babeasc

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Posted 14 May 2007 - 08:55 PM

Haha just noticed someone else posted the answer, looks like i did it wrong lol biggrin.gif
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#5 Azie

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Posted 14 May 2007 - 09:00 PM

theres not that much 2 do once u get started thank god, but here u go
sin(x) - sin(2x) = 0

replace the (sin2x) with the double angle formula so u get:
sin(x) - 2sin(x)cos(x) = 0

then take sinx as the common factor so u get:
sin(x) (1-2cos(x)) = 0

so sin(x) = 0
so x = 0

1-2cos(x) = 0
2cos(x) = 1
cos(x) = 1/2
x = 60

now so far, u have 0 and 60, but becoz the values for x range from 0 to 360, u also get 180 (180-0), 300 (360-60) and and 360 (360-0)

hope this has helped sumhow smile.gif






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