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 
July 10th, 2016, 02:29 PM  #5 
Newbie Joined: Jul 2016 From: Brazil Posts: 5 Thanks: 0  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  
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677  Quote:
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 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,976 Thanks: 1158 Math Focus: Elementary mathematics and beyond  

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