My Math Forum Sin(2*theta) into 2*theta

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 July 10th, 2016, 01:13 PM #1 Newbie   Joined: Jul 2016 From: Brazil Posts: 5 Thanks: 0 Sin(2*theta) into 2*theta Hey, I've gone a long way in this question, but I can't seem to get to the final answer. I've gotten up to sin(2*theta) = -1+(1/sqrt(2)). Doesn't seem like the double of a common angle and the question doesn't give any odd sines values. Any help would be really appreciated! Last edited by Itika; July 10th, 2016 at 01:58 PM.
 July 10th, 2016, 01:16 PM #2 Newbie   Joined: Jul 2016 From: Brazil Posts: 5 Thanks: 0 Oh, my bad! I was careless and promptly posted this thread in the wrong forums, I'm sorry. Is there any way to lock it or erase it?
 July 10th, 2016, 02:13 PM #3 Global Moderator   Joined: May 2007 Posts: 6,854 Thanks: 744 show your work.
 July 10th, 2016, 02:23 PM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 $\sin(2\theta) = 2\sin{\theta}\cos{\theta} = -2\sqrt{\dfrac{1}{4} - \dfrac{1}{8}} = -\dfrac{1}{\sqrt{2}}$ $2\theta = \arcsin\left(-\dfrac{1}{\sqrt{2}}\right) = -\dfrac{\pi}{4}$ don't worry ... a mod will move it if necessary Thanks from manus
July 10th, 2016, 02:29 PM   #5
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 Originally Posted by skeeter $\sin(2\theta) = 2\sin{\theta}\cos{\theta} = -2\sqrt{\dfrac{1}{4} - \dfrac{1}{8}} = -\dfrac{1}{\sqrt{2}}$ $2\theta = \arcsin\left(-\dfrac{1}{\sqrt{2}}\right) = -\dfrac{\pi}{4}$ don't worry ... a mod will move it if necessary
The problem is that the answer sheet shows that 2theta=15pi/4. The use of calculators is also forbidden in the exam, so using arcsin is impossible.

July 10th, 2016, 02:46 PM   #6
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 using arcsin is impossible
I did not use a calculator to find $-\dfrac{\pi}{4}$ ... it's a unit circle value.

The principle value for $2\theta = -\dfrac{\pi}{4} \implies \theta = -\dfrac{\pi}{8}$.

Since $0 \le \theta < 2\pi$, that means $\theta = \dfrac{15\pi}{8}$ is the coterminal angle in the given interval ... which means $2\theta = ?$

July 10th, 2016, 03:11 PM   #7
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 Originally Posted by Itika Oh, my bad! I was careless and promptly posted this thread in the wrong forums, I'm sorry. Is there any way to lock it or erase it?

 Tags 2theta, angle, conversion, odd, sin2theta, sine, trigonometry

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