ATAR Notes: Forum
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
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quick method
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cos(1/2) = cos(1/2)
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Do you mean basic angles if so pi/6 ?
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Do you mean basic angles if so pi/6 ?
yea like that how do you do it by hand
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Do you mean basic angles if so pi/6 ?
yea like that how do you do it by hand
You remember it.
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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
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Well, if you remember the sine values, you can remember the cosine values (they're the opposite of each other).
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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!
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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)
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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.
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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.
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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
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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 :)
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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.
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Honestly...you should just know it because you've done that many questions.
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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
(:
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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.
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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.
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I can't remember them, I just draw the triangles each and every time. Never fails me.
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Yeah i just imagine the triangles in my head every time i need to work it out.
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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
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remember the triangles, they are VERY, VERY useful
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thanks for all your help ;) ill try memorizing it