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Maths Help. Pie Qs

Rocky

Posted 07 September 2005 - 03:13 PM

Q-a Write down the exact values of sin (pie/3) and cos (pie/3.
b If tan x= 4sin (pie/3) cos (pie/3).
Find exact values of x for x for 0<= x <= 2 pie

dondon

Posted 07 September 2005 - 03:30 PM

A) youve really got to memorise the triangles for this but

2/root3
and 1/root3

B) you swap cos pi/3 and sin pi/3 with the numbers in the first bit and work it out til you get a whole number
i cant do it just now cos someones stolen my calculator


Rocky

Posted 07 September 2005 - 03:33 PM

That cool, but how did you do part A?

dondon

Posted 07 September 2005 - 03:38 PM

if you wait a minute i will draw or find a diagram and post it.

You can also do it on a calculator but you need to be able to know how to do it in your head for the noncalc paper


Rocky

Posted 07 September 2005 - 03:40 PM

That'd be really appreciated, thanx. Hope this is not wasting your time lol

dondon

Posted 07 September 2005 - 04:05 PM

wasting my time laugh.gif no not really

user posted image
that diagram gives you the corresponding number for the angles 45[deg], 30[deg] and 60[deg]

to work out the answer use trigonometry

so from them cos 60 would be 1/root3
if you can see that?!

And use the sine and cosine curves for the rest of the basic ones

sine
user posted image

cosine
user posted image

you can find out from these two where the main angles are
so from the first graph you can see that sin180 is 0

Its very comlicated to describe it


oh and can you convery angles into radians?!

Edited by dondon, 07 September 2005 - 04:20 PM.


Rocky

Posted 07 September 2005 - 04:40 PM

WTF (mind confused) lol

Dave

Posted 07 September 2005 - 04:54 PM

to work out the exact values

learn the triangles as shown in dondon's graphic

so if you are asked the exact value of sin 60

you can draw the triangle from memory

then say

sin 60 = opp/hyp = root 3 / 2

simple

dondon

Posted 07 September 2005 - 05:33 PM

exactly, if only i'd have thought of that

Rocky

Posted 07 September 2005 - 07:09 PM

So how do you do 'b' then? Like what's the technique.

dfx

Posted 07 September 2005 - 08:58 PM

b.)

Tan x = 4 Sin ( pi.gif /3 ) Cos ( pi.gif /3 ) for ( 0 lessorequal.gif x lessorequal.gif 2 pi.gif )

Tan x = 4 * ( sqrt.gif 3 /2 ) * 0.5

therefore.gif Tan x = sqrt.gif 3 implies.gif x = Tan inverse sqrt.gif 3

So, x is the tan inverse of sqrt.gif 3, which gives you ( pi.gif /3) for your first value. Now remember: because the value of X can lie anywhere between 0 and 2 pi.gif , you've also got to check elsewhere where Tan is positive. If you look to your 'CAST' diagram, you'll see Tan is also positive in the fourth quadrant (presuming your first quadrant is C, then A, then S, then T.), and for the 4th quadrant, you add your value to pi.gif , so the other value of x is [ pi.gif + ( pi.gif / 3 ) ] = 4 pi.gif / 3

therefore.gif x = ( pi.gif /3 ), (4 pi.gif /3)

ps: If you don't follow in terms of radians, convert it to degrees - it's MUCH easier to see. Once you get used to radians, you'll grow comfortable with them. Also, do try to get used to using the BBCode for symbols such as Pi, Theta, Root e.t.c. (you can find it in the smilies pop up window, and it used to be on Ally's sig.. not too sure whether it's still there lol.) But yeah, it makes the question much easier to read and get accross. Cheers.

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