Math question help (1 Viewer)

dabatman · May 3, 2017

Hi can anyone help with this math question, i've attached it below

Thanks

kawaiipotato · May 3, 2017

dabatman said:
Hi can anyone help with this math question, i've attached it below

Thanks

$\noindent $2 \sin 3 \theta = -1 \implies \sin 3 \theta = \frac{-1}{2}$$

$\noindent Note that the sine trigonometric function is periodic, so the solution to $\sin x = \frac{1}{2}$ is \\ $x = -30^{\circ} + k 2 \pi$ or $x = 180^{\circ} - (-30 ^{\circ}) + k 2 \pi = 210^{\circ} + k 2 \pi$ for any integer $k$.$

$\noindent So if $x = 3 \theta$ then the solutions for $\theta$ are \\ $\theta = -10^{\circ} + \frac{k 2 \pi}{3}$ or $\theta = 70 + \frac{k 2 \pi}{3}$.$

$\noindent Substitute appropriate $k$ values so that your $\theta$ solutions are within the required domain.$

pikachu975 · May 3, 2017

dabatman said:
Hi can anyone help with this math question, i've attached it below

Thanks

sin3theta = -1/2

Now consider the new domain of -720 <= 3theta <= 720

3theta = -30, -390, 210, 570, 330, 690
theta = -10, -130, 70, 190, 110, 230 but ignore negatives

Cant be bothered editing but drongoski posted the right solution... Did 3 times 360 wrong rip

Drongoski · May 3, 2017

0 <= 3 theta <= 1080 ??

So 3 theta = 210, 330, 210 + 360, 330 + 360, 210 + 360 + 360, 330 + 360 + 360

Therefore theta = 70, 110,190,230,310, 350

Math question help (1 Viewer)

dabatman

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kawaiipotato

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pikachu975

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Drongoski

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