Quant: sin and cos equivalents

[TNgal21]

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Hey guys. I keep having trouble finding the equivalents of sine or cosine values given in a problem.

Ex: The value of cos (pi/3) equals what? Ans: - cos (2pi/3).

During my readings I remember something about cos and sin equivalents, but at the moment can't remember where that was. Also, is this just one of those types that I should be using " All Students Take Calculus " mnemonic? Thanks for any help.

 

[DrFrankenzyme]

Hey guys. I keep having trouble finding the equivalents of sine or cosine values given in a problem.

Ex: The value of cos (pi/3) equals what? Ans: - cos (2pi/3).

During my readings I remember something about cos and sin equivalents, but at the moment can't remember where that was. Also, is this just one of those types that I should be using " All Students Take Calculus " mnemonic? Thanks for any help.

Draw out and label a unit circle. Memorize special triangles.

 

[EyEnStein 07]

cos pi/4 = sin pi/4 ...equivalent like that?

there are more..best way is unit circle though,
or the common triangles as the previous poster
mentioned.

 

[eleganteye]

cos (pi/3)= cos 60
cos 60= 1/2

idk how you got/get to -cos 2pi/3 though.

 

[EyEnStein 07]

Unless higher level math has made me forget my basics..i think cos 60 = 1/2....

ok lets try to put it in this way....a bit time consuming for a first but you can find similar techniques..(this is the quickest way i can think of the proof)

So anyways...we have Cos(pi/3) first....imagine graphing a vector on a coordinate system (only consisting of quadrant I and II..so its like _|_ )
that has 60 degrees between the vector and the "x" axis.

Now imagine on the same graph...drawing a vector that is 120degrees from the same x -axis (on the first quadrant)...you will realize that you just drew the same vector as a reflection on the y axis. Clearly...these 2 are equal but opposite. So now...you can think about it like this...Cos 60 (well known) is 1/2 right? now if the 2nd vector of 120degrees is EQUAL but opposite...then its - 1/2.

But we need to know what Pi/3 equals....and if we just add a (-) sign in front of cos (120) or cos(2pi/3) then..we get + 1/2.


EDIT: if this really gives you that much trouble....make this your new bestfriend: