and

sin[arcsin 2/3]
       ------
           2

thats 2 thirds divided by two

points will be given out for an exact answer with work explained!

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Post edited at 9:13 pm on Dec. 3, 2008 by what the mong

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cos(arccos 8) = 8

You wrote arccot... was that a typo, or is that actually what you need to solve?  I solved for arc cos.

sin[arcsin 2/3]  = 1/3
      ------
          2

Do you know what the relationship between sin and arc sin is... or the relationship between cos and arc cos?

Basically... they are inverse's of one another.  So... if...

cos x = y  then...
arccos y = x

This being said, when you take the cos or arccos, it's just the number that you have there.  Let's take the general case.

Let...
cos y = x... then, by definition
arccos x = y

so... what is cos(arccos x)?

Well... arccos x = y.  So we plug that in, and we get...

cos(arccos x) = cos (y).  From above, we stated that cos y = x.

Therefore... cos y = x.

Using that in your first problem... the answer would just be 8 (if it was arc cos)

Similar steps are taken for the second problem.  So it would just be (2/3)/2