Posted 07 September 2005 - 03:13 PM
b If tan x= 4sin (pie/3) cos (pie/3).
Find exact values of x for x for 0<= x <= 2 pie
Posted 07 September 2005 - 03:30 PM
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
Posted 07 September 2005 - 03:38 PM
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
Posted 07 September 2005 - 03:40 PM
Posted 07 September 2005 - 04:05 PM
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
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.
Posted 07 September 2005 - 04:54 PM
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
sin 60 = opp/hyp = root 3 / 2
If i am not here i am somewhere else
Posted 07 September 2005 - 07:09 PM
Posted 07 September 2005 - 08:58 PM
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.
1 user(s) are reading this topic
0 members, 1 guests, 0 anonymous users