Author Topic: Evaluate cos(pi/8) (Read 12271 times) Tweet Share

jasopan · « **on:** April 17, 2010, 05:56:26 pm »

Evalaluate cos(pi/8) using half angle Formulae leaving answer in exact values

Thanks!

brightsky · « **Reply #1 on:** April 17, 2010, 06:01:31 pm »

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

Use half-angle formula: $\cos^2\left(\frac{x}{2}\right) = \frac{1}{2} \left(1 + \cos(x)\right)$

In this case: $x = \frac{\pi}{4}$

So $\cos^2 \left(\frac{\frac{\pi}{4}}{2}\right) = \frac{1}{2} \left(1 + \cos(\frac{\pi}{4}\right)$

$\cos \left(\frac{\frac{\pi}{4}}{2}\right) = \sqrt{\frac{1}{2} \left(1 + \cos(\frac{\pi}{4}\right)}$

So:

$\implies \sqrt{1 + \frac{\sqrt{2}}{2}}$

jasopan · « **Reply #2 on:** April 17, 2010, 06:05:00 pm »

^^ Yup, got the sin cos ones, but now I'm stuck on the tan
I can't seem to use the formula, or should i do
tanx=sinx/cosx and then simplify?

And also is there a way to solve the sin(pi/8) using sinX=2sin(x/2)cos(X/2)
Thanks again

tram · « **Reply #3 on:** April 17, 2010, 09:59:00 pm »

there is another way to evaluate sin(pi/8) and cos(pi/8) using complex numbers if anyone is interested. In fact, it make a a rather good question. It's in the essentials book, pg 168, Q8

physics · « **Reply #4 on:** April 17, 2010, 10:35:19 pm »

Quote from: brightsky on April 17, 2010, 06:01:31 pm

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

Use half-angle formula: $\cos^2\left(\frac{x}{2}\right) = \frac{1}{2} \left(1 + \cos(x)\right)$

In this case: $x = \frac{\pi}{4}$

So $\cos^2 \left(\frac{\frac{\pi}{4}}{2}\right) = \frac{1}{2} \left(1 + \cos(\frac{\pi}{4}\right)$

$\cos \left(\frac{\frac{\pi}{4}}{2}\right) = \sqrt{\frac{1}{2} \left(1 + \cos(\frac{\pi}{4}\right)}$

So:

$\implies \sqrt{1 + \frac{\sqrt{2}}{2}}$

sucky uni maths stuff

its so hard D:

tram · « **Reply #5 on:** April 17, 2010, 10:46:35 pm »

lol, uni maths stull is AWESOME, and that not uni maths, it's spech

physics · « **Reply #6 on:** April 17, 2010, 10:48:30 pm »

Quote from: tram on April 17, 2010, 10:46:35 pm

lol, uni maths stull is AWESOME, and that not uni maths, it's spech

we're doing this at uni maths D: i dont do spesh so i not know haha

tram · « **Reply #7 on:** April 17, 2010, 10:51:32 pm »

wtf, i just realised that. How are you doing uni maths without spech? not only how but why???

physics · « **Reply #8 on:** April 17, 2010, 10:53:12 pm »

Quote from: tram on April 17, 2010, 10:51:32 pm

wtf, i just realised that. How are you doing uni maths without spech? not only how but why???

how because they let me..i dont know y every1 says u have to do spesh b4 uni maths :S but they let me
WHY? so i can drop a subject and profit in free hours haha

brightsky · « **Reply #9 on:** April 17, 2010, 11:01:44 pm »

Quote from: tram on April 17, 2010, 09:59:00 pm

there is another way to evaluate sin(pi/8) and cos(pi/8) using complex numbers if anyone is interested. In fact, it make a a rather good question. It's in the essentials book, pg 168, Q8

Can you post up the proof?

tram · « **Reply #10 on:** April 17, 2010, 11:05:54 pm »

reli? dammit i hate latex have never used it cos i ceebes

brightsky · « **Reply #11 on:** April 17, 2010, 11:07:20 pm »

Quick outline? Just to quench my curiosity?

TrueTears · « **Reply #12 on:** April 17, 2010, 11:08:14 pm »

latex is the bomb, once u get into uni latex is ur best friend for maths xD might as well learn the skill now

tram · « **Reply #13 on:** April 17, 2010, 11:11:36 pm »

i'll take you thu the logic you'll learn more by doing the numbers youself(and it'll save me time lol)

ok

1)It's the same logic as questions 3 and 4. Let z^2 be 1+i and let z be a+bi
2) square (a+bi) and let it equal 1+i, solve for a and b

part ii) you should be able to do, it's pretty standard, just basic using de moirves

part b)

1) expand the and from part aii into carterian form, not symplyfing cos(pi/8) and sin(pi/8)
2) equate coefficents

Hope that helps:) Ask if you need more help

brightsky · « **Reply #14 on:** April 17, 2010, 11:14:09 pm »

Lol I don't have the book.

Search the forums now!

We have moved!

Author Topic: Evaluate cos(pi/8) (Read 12271 times) Tweet Share

jasopan

Evaluate cos(pi/8)

brightsky

Re: Evaluate cos(pi/8)

jasopan

Re: Evaluate cos(pi/8)

tram

Re: Evaluate cos(pi/8)

physics

Re: Evaluate cos(pi/8)

tram

Re: Evaluate cos(pi/8)

physics

Re: Evaluate cos(pi/8)

tram

Re: Evaluate cos(pi/8)

physics

Re: Evaluate cos(pi/8)

brightsky

Re: Evaluate cos(pi/8)

tram

Re: Evaluate cos(pi/8)

brightsky

Re: Evaluate cos(pi/8)

TrueTears

Re: Evaluate cos(pi/8)

tram

Re: Evaluate cos(pi/8)

brightsky

Re: Evaluate cos(pi/8)

Recent Posts

User:
Password: