Question

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 2-the square root of 2/4

***My Answer: D***

Answer 1

Nope

Answer 2

Dangit hahaha. My second choice would have to be A then

Answer 3

Nope again, ahhahha

Answer 4

Dangit(lol)...Not the best at trig identities. Sorry

Answer 5

ok, hint 17pi/8 = 16pi/8 + pi/8

Answer 6

and you have the perfect angle 16pi/8 = 2pi

Answer 7

break it out by cos (a+b) =....

Answer 8

How would I find the a and b?

Answer 9

Would it just be a= 16pi/8 and b= pi/8?

Answer 10

hey, \(cos (\dfrac{17\pi}{8}=cos (\dfrac{16\pi +\pi}{8}\)

Answer 11

yup

Answer 12

Oh I see. Ok

Answer 13

So from there we get it into the form...\[\cos(\frac{ 16\pi }{ 8 })\cos(\frac{ \pi }{ 8 }) + \sin(\frac{ 16\pi }{ 8 })\sin(\frac{ \pi }{ 8 })\]

Answer 14

I think

Answer 15

@Loser66 Now this is the part that I have trouble understanding. I do not know where to go from here

Answer 16

whyyyyyyyyy? 16pi/8 = 2pi, right?

Answer 17

Yes

Answer 18

cos 2pi =1, right?

Answer 19

sin 2pi =0, ok?

Answer 20

Ok

Answer 21

so, at the end, you just have cos (pi/8 ) =0.99999

Answer 22

Ohhhhhh ok! That was my problem all along! I would divide pi/8 without the cos! Haha Thank you so much!

Answer 23

ok

Answer 24

What the... my computer just told me that it was A :(

Answer 25

Facepalm. hehehe... let's get other's help @campbell_st

Answer 26

\(\dfrac{17\pi}{8} = \dfrac{16\pi}{8} + \dfrac{\pi}{8} = 2\pi + \dfrac{\pi}{8}\)

\(\cos \dfrac{17\pi}{8} = \cos 2\pi + \dfrac{\pi}{8} = \cos \dfrac{\pi}{8} \)

\(\Large \cos \dfrac{\pi}{8} = \cos \left ( {\dfrac{\frac{\pi}{4}}{2} } \right)\)

\(\cos \dfrac{\theta}{2} = \sqrt{\dfrac{1}{2}(1 + \cos \theta) }\)

\(\Large \cos \dfrac{\pi}{8} = \cos \left ( {\dfrac{\frac{\pi}{4}}{2} } \right)

= \sqrt{\dfrac{1}{2}(1 + \cos \dfrac{\pi}{4})}\)

\(= \sqrt{\dfrac{1}{2} (1 + \dfrac{\sqrt{2}}{2})} = {\sqrt{\dfrac{1}{2} + \dfrac{\sqrt{2}}{4}}} \)

\(= \sqrt{\dfrac{2 + \sqrt 2}{4}} = \dfrac{\sqrt{2 + \sqrt 2 } }{ 2 }\)

Answer 27

WWWWWWWWWWWWoooooah!!! It is much.... more logic than my way. Thank you so much @mathstudent55

Answer 28

You're welcome.

Answer 29

@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.