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anonymous
 one year ago
Find the exact value by using a halfangle identity.
cosine (5pi/12)
anonymous
 one year ago
Find the exact value by using a halfangle identity. cosine (5pi/12)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{5\pi}{12}\] is half of \[\frac{5\pi}{6}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then, 5pi/6 = √3/2 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\cos^2(\frac{1}{2} \theta)=\frac{1}{2}(1+\cos(\theta)) \\ \text{ you have determined } \theta=\frac{5\pi}{6} \\ \text{ and I think you are actually saying } \cos(\frac{5\pi}{6})=\frac{\sqrt{3}}{2} \\ \text{ because } \frac{5\pi}{6} \neq \frac{\sqrt{3}}{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the answer maybe be cos(5pi/12) = √2  2√3 /(fraction) 2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438812995121:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so you have: \[\cos^2(\frac{5\pi}{12})=\frac{1}{2}(1+\frac{\sqrt{3}}{2})\] you just need to solve for cos(5pi/12) above notice I just replaced theta with 5pi/6 and replaced cos(5pi/6) with sqrt(3)/2 \[\cos^2(\frac{5\pi}{12})= \frac{1}{2}(\frac{2}{2}\frac{\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{1}{2}(\frac{2\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{2\sqrt{3}}{4}\] now take square root of both sides

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you are going to choose the positive output because 5pi/12 is between 0 and pi/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for 2  √3 / 4 what do you mean by square root both sides?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you want to find cos(5pi/12)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, oh okay so could it be cos(5pi/12) = 2  √3 / 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well you are missing the square root on top

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\cos^2(\frac{5\pi}{12})= \frac{1}{2}(\frac{2}{2}\frac{\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{1}{2}(\frac{2\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{2\sqrt{3}}{4} \\ \text{ take square root of both sides } \\ \cos(\frac{5\pi}{12})= \sqrt{\frac{2\sqrt{3}}{4}} \text{ note: chose positive \because } 0<\frac{5\pi}{12}<\frac{\pi}{2} \\ \cos(\frac{5\pi}{12})=\frac{\sqrt{2 \sqrt{3}}}{\sqrt{4}}=\frac{\sqrt{2 \sqrt{3}}}{2}\]
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