Trig Equation (1 Viewer)

coyazayo · Jul 10, 2016

Hi.

Evaluate the general solution of following trigonometric equations.

sin(3x-pi/4)+cos(x+pi/3)=0

leehuan · Jul 10, 2016

Um, what. I would use sum to product like follows but if this was a 3U question it's seriously pushing it.

$\begin{align*}\sin \left(3x-\frac{\pi}{4}\right)+\cos \left(x+\frac{\pi}{3}\right)&=0\\ \sin \left(3x-\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{6}-x\right) &=0 \\2\sin \left( \frac { 2x-\frac { \pi }{ 12 } }{ 2 } \right) \cos \left( \frac { 4x-\frac { 5\pi }{ 12 } }{ 2 } \right) &=0\end{align*}$

Which would then become this I think

$x-\frac{\pi}{24}=k\pi \iff x=n\pi + \frac{\pi}{24}$

or
$2x-\frac{5\pi}{24}=k\pi \pm \frac{\pi}{2} \iff 2x = k\pi + \frac{5\pm 12}{24}\pi \iff x=\frac{k\pi}{2}+\frac{(5\pm 12)\pi}{48}$

InteGrand · Jul 10, 2016

HSC would probably first ask you to show the sum to product identity.

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Trig Equation (1 Viewer)

coyazayo

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leehuan

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InteGrand

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