anonymous
  • anonymous
Find the exact value by using a half-angle identity. cosine (5pi/12)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\frac{5\pi}{12}\] is half of \[\frac{5\pi}{6}\]
anonymous
  • anonymous
then, 5pi/6 = -√3/2 ?
freckles
  • freckles
\[\cos^2(\frac{1}{2} \theta)=\frac{1}{2}(1+\cos(\theta)) \\ \text{ you have determined } \theta=\frac{5\pi}{6} \\ \text{ and I think you are actually saying } \cos(\frac{5\pi}{6})=\frac{-\sqrt{3}}{2} \\ \text{ because } \frac{5\pi}{6} \neq \frac{-\sqrt{3}}{2}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
would the answer maybe be cos(5pi/12) = √2 - 2√3 /(fraction) 2 ?
freckles
  • freckles
what does that say
anonymous
  • anonymous
|dw:1438812995121:dw|
freckles
  • freckles
so 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
  • freckles
you are going to choose the positive output because 5pi/12 is between 0 and pi/2
anonymous
  • anonymous
so i wasnt right D:
anonymous
  • anonymous
for 2 - √3 / 4 what do you mean by square root both sides?
freckles
  • freckles
you want to find cos(5pi/12)
freckles
  • freckles
not cos^2(5pi/12)
anonymous
  • anonymous
oh, oh okay so could it be cos(5pi/12) = 2 - √3 / 2
freckles
  • freckles
well you are missing the square root on top
freckles
  • freckles
\[\cos^2(\frac{5\pi}{12})= \frac{1}{2}(\frac{2}{2}-\frac{\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{1}{2}(\frac{2-\sqrt{3}}{2}) \\ \cos^2(\frac{5\pi}{12})=\frac{2-\sqrt{3}}{4} \\ \text{ take square root of both sides } \\ \cos(\frac{5\pi}{12})= \sqrt{\frac{2-\sqrt{3}}{4}} \text{ note: chose positive \because } 0<\frac{5\pi}{12}<\frac{\pi}{2} \\ \cos(\frac{5\pi}{12})=\frac{\sqrt{2- \sqrt{3}}}{\sqrt{4}}=\frac{\sqrt{2- \sqrt{3}}}{2}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.