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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: sachinmachin on September 30, 2009, 07:11:03 pm

Title: pi/8
Post by: sachinmachin on September 30, 2009, 07:11:03 pm: $\frac{\pi }{8}$

what 2 angles produce this for a compound angle formula??
Title: Re: pi/8
Post by: kurrymuncher on September 30, 2009, 07:13:35 pm: If your wondering how to break this up, dont, because you cant. Im guessing this should be used in a tan or sin double angle formula, so make Pi/8 equal Thetha, and then use the formulas.
Title: Re: pi/8
Post by: dejan91 on September 30, 2009, 07:15:42 pm: Double angle forumula...?

EDIT: ...didn't read kurrymuncher's post.
Title: Re: pi/8
Post by: TrueTears on September 30, 2009, 07:15:55 pm: If you're trying to evualate $\cos(\frac{\pi}{8})$ or $\sin(\frac{\pi}{8})$ , I'd use the half angle formula.

Ie, $\sin(\frac{\pi}{8}) = \sin(\frac{1}{2} \times \frac{\pi}{4})$
Title: Re: pi/8
Post by: sachinmachin on September 30, 2009, 07:20:05 pm: Quote from: kurrymuncher on September 30, 2009, 07:13:35 pm
If your wondering how to break this up, dont, because you cant. Im guessing this should be used in a tan or sin double angle formula, so make Pi/8 equal Thetha, and then use the formulas.
twas in heffernan 09 exam 1 which we did as a trial exam at school. i was convinced that it was a compound angle formula question as it asked:

Show that $cos(\frac{\pi }{8}) =$ something, lol i forgot. (it was a surd of some sort)
Title: Re: pi/8
Post by: sachinmachin on September 30, 2009, 07:21:46 pm: Quote from: TrueTears on September 30, 2009, 07:15:55 pm
If you're trying to evualate $\cos(\frac{\pi}{8})$ or $\sin(\frac{\pi}{8})$ , I'd use the half angle formula.

Ie, $\sin(\frac{\pi}{8}) = \sin(\frac{1}{2} \times \frac{\pi}{4})$

yeh i suppose your right TT. i really do suck:(
Title: Re: pi/8
Post by: TrueTears on September 30, 2009, 07:22:28 pm: $\cos^2 \left(\frac{x}{2} \right) = \frac{1}{2} \left( 1 + \cos(x) \right)$

And then you can sub in $\frac{\pi}{4}$ in there. :)

[Be careful what answer you pick, make sure you read the question to decide which quadrant it's in]
Title: Re: pi/8
Post by: sachinmachin on September 30, 2009, 07:24:35 pm: Quote from: TrueTears on September 30, 2009, 07:22:28 pm
$\cos^2 \left(\frac{x}{2} \right) = \frac{1}{2} \left( 1 + \cos(x) \right)$

And then you can sub in $\frac{\pi}{4}$ in there. :)

[Be careful what answer you pick, make sure you read the question to decide which quadrant it's in]

makes so much more sense now. thankyou TT
Title: Re: pi/8
Post by: dejan91 on September 30, 2009, 07:28:44 pm: TrueTears, I swear.... Stop being so quick on the posts! Was posting the exact same thing but am just 10x slower on latex.....

I'm gonna post anyway so my time doen't go to waste :P :

$cos (2x) = 2 cos^2 (x)-1$
$cos(x) = \sqrt {\frac{1}{2}(cos((2x) + 1)}$

And use $x = \frac {\pi}{8}$ .
Title: Re: pi/8
Post by: TrueTears on September 30, 2009, 07:31:34 pm: Quote from: dejan91 on September 30, 2009, 07:28:44 pm
TrueTears, I swear.... Stop being so quick on the posts! Was posting the exact same thing but am just 10x slower on latex.....

I'm gonna post anyway so my time doen't go to waste :P :

$cos (2x) = 2 cos^2 (x)-1$
$cos(x) = \sqrt {\frac{1}{2}(cos((2x) + 1)}$

And use $x = \frac {\pi}{8}$ .

hahahahahaha sorry! :(
Title: Re: pi/8
Post by: dejan91 on September 30, 2009, 07:34:15 pm: Quote from: TrueTears on September 30, 2009, 07:31:34 pm
Quote from: dejan91 on September 30, 2009, 07:28:44 pm
TrueTears, I swear.... Stop being so quick on the posts! Was posting the exact same thing but am just 10x slower on latex.....

I'm gonna post anyway so my time doen't go to waste :P :

$cos (2x) = 2 cos^2 (x)-1$
$cos(x) = \sqrt {\frac{1}{2}(cos((2x) + 1)}$

And use $x = \frac {\pi}{8}$ .

hahahahahaha sorry! :(
:P