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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: tha boss on October 21, 2011, 05:38:43 pm

Title: without calculator solving e.g. cos (1/2)
Post by: tha boss on October 21, 2011, 05:38:43 pm
quick method
Title: Re: without calculator solving e.g. cos (1/2)
Post by: TrueTears on October 21, 2011, 06:02:52 pm
cos(1/2) = cos(1/2)
Title: Re: without calculator solving e.g. cos (1/2)
Post by: onur369 on October 21, 2011, 06:30:43 pm
Do you mean basic angles if so pi/6 ?
Title: Re: without calculator solving e.g. cos (1/2)
Post by: tha boss on October 21, 2011, 07:40:13 pm
Do you mean basic angles if so pi/6 ?
yea like that how do  you do it by hand
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Truck on October 21, 2011, 08:06:17 pm
Do you mean basic angles if so pi/6 ?
yea like that how do  you do it by hand

You remember it.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: tha boss on October 21, 2011, 08:17:45 pm
Do you mean basic angles if so pi/6 ?
yea like that how do  you do it by hand

You remember it.
i cant its too much man
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Hutchoo on October 21, 2011, 08:18:32 pm
Well, if you remember the sine values, you can remember the cosine values (they're the opposite of each other).
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Truck on October 21, 2011, 08:41:43 pm
Do you mean basic angles if so pi/6 ?
yea like that how do  you do it by hand

You remember it.
i cant its too much man

Sorrys dude, stare at it for a while, write it out, get someone to repeatedly ask you values (shoot them at you) and you should get it after a while. Gotta love rote memorization!
Title: Re: without calculator solving e.g. cos (1/2)
Post by: xZero on October 21, 2011, 08:48:03 pm
just fyi. cos(1/2) is just cos(1/2)

if you want to remember the table, just memorise sine(theta), cos(theta) is just the reverse of that and tan(theta) is just sin(theta)/cos(theta)
Title: Re: without calculator solving e.g. cos (1/2)
Post by: thushan on October 21, 2011, 08:50:47 pm
Try this:

                  0                30                   45                    60                  90
sin        root(0)/2     root(1)/2       root(2)/2          root(3)/2         root(4)/2

cos      root(4)/2     root(3)/2        root(2)/2          root(1)/2         root(0)/2


Note: root(0)/2 = 0, root(1)/2 = 1, root(4)/2 = 2/2 = 1.

To get tan, use sin/cos.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: BlueSky_3 on October 21, 2011, 09:46:12 pm
Or just derive them each time by drawing up a right-angled triangle, 2 since one for pi/3 and pi/6 and another for pi/4.
Over time you should be able to do them in your head. 
Title: Re: without calculator solving e.g. cos (1/2)
Post by: luffy on October 22, 2011, 11:37:01 am
Try this:

                  0                30                   45                    60                  90
sin        root(0)/2     root(1)/2       root(2)/2          root(3)/2         root(4)/2

cos      root(4)/2     root(3)/2        root(2)/2          root(1)/2         root(0)/2


Note: root(0)/2 = 0, root(1)/2 = 1, root(4)/2 = 2/2 = 1.

To get tan, use sin/cos.

root(1)/2 = 1? :P
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Asx4Life on October 22, 2011, 11:53:40 am
Construct your own table before starting an exam. This is how I used to construct a table before remembering trig values.
1. label your table           
                  0          30        45         60           90
sin
cos
2.  Go along the sin row numbering each one from 0-4                 
                 0          30         45         60           90
sin            0           1           2            3           4
cos
3. Label the cos row backwards
                 0          30         45         60           90
sin            0           1           2            3            4
cos           4           3           2            1            0
4.Put a square root on all the values
                 0          30         45         60           90
sin            r0          r1         r2          r3            r4                          r=square root
cos           r4          r3         r2           r1           r0
5.Divide all values by 2
                 0          30         45         60           90
sin            (r0)/2    (r1)/2   (r2)/2     (r3)/2      (r4)/2
cos           (r4)/2   (r3)/2    (r2)/2     (r1)/2      (r0)/2

And you got your table! This takes less than 10 seconds if u do it fast :)
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Lasercookie on October 22, 2011, 11:58:58 am
I found it easier to just memorise the little triangle for 30, 45 and 60. You would probably already know the values for sin, cos and tan 0 and 90 off the top of your head anyway.

Title: Re: without calculator solving e.g. cos (1/2)
Post by: REBORN on October 22, 2011, 11:59:41 am
Honestly...you should just know it because you've done that many questions.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: monkeywantsabanana on October 22, 2011, 12:54:40 pm
You can use the Hand Trick!

Our teacher showed us this, the rapping starts at 1:00 - http://www.youtube.com/watch?v=mg8IDXpmc-U

(:
Title: Re: without calculator solving e.g. cos (1/2)
Post by: onur369 on October 22, 2011, 05:12:22 pm
To be honest I do it in a wierd way. pi/6 = 180/6=30 , pi/4=180/4=45, pi/2=90 pi is 180...
For the balues like sin pi/6= 1/2 I think of it this way.  Increase the numerator by one and square root it. sin(pi/6) = sq(1)/2 =1/2 and then sin(pi/4) = sq(2)/2 than sin(pi/3)= sq(3)/2
For cos I decrease the value of numerator by one, cos(pi/6) = sq(3)/2  cos(pi/4)= Sq(2)/2 and cos(pi/2) = Sq(1)/2=1/2, as squareroot of 1 is 1.

Its weird but it works.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: b^3 on October 22, 2011, 05:16:38 pm
The way I do it is to think the small angle means cos is big and sin is small, and the large angle means cos is small and sin is big.
i.e. small=1/2
big =root(3)/2
e.g. sin(pi/6) is smalll angle, so sin is small so 1/2
e.g. cos(5pi/6)=-cos(pi/6) so small angle, so cos is big so root(3)/2
Just remember to apply CAST for the correct signs.

My method is a bit confusing but it works for me, I like to visualise it in my head when I do it.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: taiga on October 22, 2011, 05:51:56 pm
I can't remember them, I just draw the triangles each and every time. Never fails me.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: tony3272 on October 22, 2011, 05:59:45 pm
Yeah i just imagine the triangles in my head every time i need to work it out.
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Hutchoo on October 22, 2011, 08:26:11 pm
You can use the Hand Trick!

Our teacher showed us this, the rapping starts at 1:00 - http://www.youtube.com/watch?v=mg8IDXpmc-U

(:
lol. Remembering that rap is probably harder than remembering the ratios/exact values :P
Title: Re: without calculator solving e.g. cos (1/2)
Post by: Anon123 on October 22, 2011, 11:49:36 pm
remember the triangles, they are VERY, VERY useful
Title: Re: without calculator solving e.g. cos (1/2)
Post by: tha boss on October 23, 2011, 12:45:03 am
thanks for all your help  ;) ill try memorizing it