A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
What is the exact value of cos 17pi/8?
a) square root of 2+the square root of 2/4
b.) 0.38
c.) 0.99
d.)square root of 2the square root of 2/4
***My Answer: D***
anonymous
 one year ago
What is the exact value of cos 17pi/8? a) square root of 2+the square root of 2/4 b.) 0.38 c.) 0.99 d.)square root of 2the square root of 2/4 ***My Answer: D***

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Dangit hahaha. My second choice would have to be A then

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Dangit(lol)...Not the best at trig identities. Sorry

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1ok, hint 17pi/8 = 16pi/8 + pi/8

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1and you have the perfect angle 16pi/8 = 2pi

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1break it out by cos (a+b) =....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would I find the a and b?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would it just be a= 16pi/8 and b= pi/8?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1hey, \(cos (\dfrac{17\pi}{8}=cos (\dfrac{16\pi +\pi}{8}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So from there we get it into the form...\[\cos(\frac{ 16\pi }{ 8 })\cos(\frac{ \pi }{ 8 }) + \sin(\frac{ 16\pi }{ 8 })\sin(\frac{ \pi }{ 8 })\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 Now this is the part that I have trouble understanding. I do not know where to go from here

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1whyyyyyyyyy? 16pi/8 = 2pi, right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1so, at the end, you just have cos (pi/8 ) =0.99999

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhhhhh ok! That was my problem all along! I would divide pi/8 without the cos! Haha Thank you so much!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What the... my computer just told me that it was A :(

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Facepalm. hehehe... let's get other's help @campbell_st

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{17\pi}{8} = \dfrac{16\pi}{8} + \dfrac{\pi}{8} = 2\pi + \dfrac{\pi}{8}\) \(\cos \dfrac{17\pi}{8} = \cos 2\pi + \dfrac{\pi}{8} = \cos \dfrac{\pi}{8} \) \(\Large \cos \dfrac{\pi}{8} = \cos \left ( {\dfrac{\frac{\pi}{4}}{2} } \right)\) \(\cos \dfrac{\theta}{2} = \sqrt{\dfrac{1}{2}(1 + \cos \theta) }\) \(\Large \cos \dfrac{\pi}{8} = \cos \left ( {\dfrac{\frac{\pi}{4}}{2} } \right) = \sqrt{\dfrac{1}{2}(1 + \cos \dfrac{\pi}{4})}\) \(= \sqrt{\dfrac{1}{2} (1 + \dfrac{\sqrt{2}}{2})} = {\sqrt{\dfrac{1}{2} + \dfrac{\sqrt{2}}{4}}} \) \(= \sqrt{\dfrac{2 + \sqrt 2}{4}} = \dfrac{\sqrt{2 + \sqrt 2 } }{ 2 }\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1WWWWWWWWWWWWoooooah!!! It is much.... more logic than my way. Thank you so much @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1@Loser66 You were trying to use the identity for the cosine of a sum of angles. That method does not work in this problem. That method works if you can break up the angle into two angles whose cosines you know. The problem here is that the cos of pi/8 is not one of the know values. On the other hand, the cos of pi/4 is well known, so using the identity of the cosine of a half angle gives you the result.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.