[Rocky]

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]

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]

That cool, but how did you do part A?

[dondon]

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]

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

[dondon]

wasting my time no not really


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


cosine


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]

WTF (mind confused) lol

[Dave]

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]

exactly, if only i'd have thought of that

[Rocky]

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

[dfx]

b.)

Tan x = 4 Sin ( /3 ) Cos ( /3 ) for ( 0 x 2 )

Tan x = 4 * ( 3 /2 ) * 0.5

Tan x = 3 x = Tan inverse 3

So, x is the tan inverse of 3, which gives you ( /3) for your first value. Now remember: because the value of X can lie anywhere between 0 and 2 , 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 , so the other value of x is [ + ( / 3 ) ] = 4 / 3

x = ( /3 ), (4 /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.