Question

What is the exact value of 11pi/8? (with steps please) :)

Answer 1

11π/8 is an exact value.

where does the trig part of your question come in?
Was is something like sin (11π/8) ?

Answer 2

yea what reiny said

Answer 3

Oh I'm sorry. It's cosine (11pi/8) :)

Answer 4

Not sure if you are better thinking in terms of degrees or radians, most people are more familiar with degrees
11π/8 radians = 247.5°

so cos(11π/8) = cos(247.5°) (in quad III)
= -cos 67.5

let that sit.

67.5 = 90-22.5
cos 67.5 = cos(90-22.5)
= sin 22.5 (complementary angles property, e.g. sin 20 = cos70 )

using cos 2A = 1 - 2sin^2 A
cos 45 = 1 - 2sin^2 (22.5)
√2 /2 = 1 - 2sin^2 (22.5)
2 sin^2 22.5 = 1 - √2/2 = (2-√2)2
sin^2 22.5 = (2-√2)/4
sin 22.5 = √(2-√2)/2

so recall we needed
- cos67.5
= -sin22.5
= - √(2-√2)/2

<b>cos (11π/8) = -√(2-√2)/2</b>

check:
-√(2-√2)/2 = appr. -.38268...
cos 247.5 = -.3826..
How about that ???

Answer 5

It's good but there is a typo... The line with the typo that does not make sense is:

2 sin^2 22.5 = 1 - √2/2 = (2-√2)2

...it should read:

2 sin^2 22.5 = 1 - √2/2 = (2-√2)/2

The whole process after that is legit.

(And here is the edited version, below:)

using cos 2A = 1 - 2sin^2 A
cos 45 = 1 - 2sin^2 (22.5)
√2 /2 = 1 - 2sin^2 (22.5)
2 sin^2 22.5 = 1 - √2/2 = (2-√2)/2
sin^2 22.5 = (2-√2)/4
sin 22.5 = √(2-√2)/2

so recall we needed
- cos67.5
= -sin22.5
= - √(2-√2)/2

cos (11π/8) = -√(2-√2)/2