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2004 P1 Q3 - HSN forum

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2004 P1 Q3


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#1 Adam

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Posted 17 May 2006 - 08:40 PM

Here's what I done:

tanx^2 = 3
tanx = root3

=> pi.gif/3

tan is positive in the 1st and 4th quadrants, so x = pi.gif/3 and 4IPB Image/3

But the answers say that x is also equal to 2IPB Image/3 and 5IPB Image/3. Where do these answers come from, and why? huh.gif

Cheers.

#2 George

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Posted 17 May 2006 - 08:47 PM

You need to take care with square roots:



\begin{align*}(\tan x)^2 &= 3 \\
\Rightarrow \tan x &= \pm \sqrt3\end{align*}

The \pm is important, since that means you now look for solutions in all 4 quadrants, using the CAST diagram.

Do you see where the other solutions come from now?

#3 Adam

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Posted 17 May 2006 - 08:56 PM

Ahhh... gotcha. Silly me.

Thanks. smile.gif





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