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 June 13th, 2010, 12:33 AM #1 Newbie   Joined: May 2010 Posts: 4 Thanks: 0 goniometric equation pls help Determine the solutions goniometric equations in G = [0 2? [ a) 2sin(x)=1/cos(x) b)cos2(x)-sin2(x)=0.4 [quote] cos squar(x )minus sin squar(x )is equal to 0,4
June 13th, 2010, 03:50 AM   #2
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Re: goniometric equation

Hello, ibros06!

Quote:
 $\text{Solve for }x:\;\;x \in [0,\:2\pi]$ [color=beige]. . [/color]$(a)\;\; 2\sin x \:=\:\frac{1}{\cos x}$

$\text{We have: }\;2\,\sin x\,\cos x \:=\:1 \;\;\;\Rightarrow\;\;\;\sin2x \:=\:1$

$\text{Then: }\;2x \:=\:\sin^{-1}(1) \;=\; \frac{\pi}{2},\;\frac{5\pi}{2},\; \frac{\9\pi}{2},\;\cdots$

$\text{Therefore: }\;x \;=\;\frac{\pi}{4},\;\frac{5\pi}{4}$

Quote:
 $(b)\;\;\cos^2 x \,-\, \sin^2x \:=\:0.4$

$\text{We have: }\;\cos2x \:=\:0.4$

$\text{Then: }\;2x \;=\; \cos^{-1}(0.4) \;=\;\begin{Bmatrix}\;1.159279481\; \\ \\ \\ \\ \;5.123905826\; \end{Bmatrix}$

$\text{Therefore: }\;x \;=\;\begin{Bmatrix}\;0.579639741\; \\ \\ \\ \\ \;2.561952913\; \end{Bmatrix}$

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