math help/question

[SparklyUnicorn]

At the risk of looking dumb....

 

- ln (cos (Pi/4) )

 

I know the cos part is square root of 2 over 2.  I think I vaguely remember the details of that.  The answer was written as 1/2 ln 2.  Why/how?  For some reason I'm not remembering anything that gets me to that point. 

 

This was part of a larger problem.  I'm just stuck at that final part.  And what should I review related to that?

 

Ugh.  It's like I forgot everything.  So this past week I have gone through all my calc 1 notes and reviewed some trig stuff.  I'm starting to feel like it is coming back to me.  Not sure I have room for anymore information.  LOL

 

Thanks

 

 

 

 

 

[Arcadia]

square root of 2 over 2 = 2^(-1/2)

 

- ln (cos (Pi/4) ) = - ln ( 2^(-1/2))

= - (-1/2) ln 2

= (1/2) ln 2

[SparklyUnicorn]

That's fabulous.  Thank you so much!

 

[Arcadia]

And what should I review related to that?

...

So this past week I have gone through all my calc 1 notes and reviewed some trig stuff. I'm starting to feel like it is coming back to me. Not sure I have room for anymore information.

You need this Sparknotes Calculus I cheat sheet for mom fog days :)

http://www.sparknotes.com/free-pdfs/nook-study/9781411487628_calculusi.pdf

[regentrude]

  And what should I review related to that?

 

Laws of logarithms.

[SparklyUnicorn]

Laws of logarithms.

 

Yep!  LOL

 

After seeing that I printed them out.  My kid remembers them. Me?  Not so much.

 

If I could combine his brain and my worth ethic we'd rule the universe.  :laugh:

 

What I don't always understand though is how far to take an answer.  I might have just left it the way it was.  I don't always know what comes next.  That would help so maybe it'll become clearer to me (eventually). 

[SparklyUnicorn]

You need this Sparknotes Calculus I cheat sheet for mom fog days :)

http://www.sparknotes.com/free-pdfs/nook-study/9781411487628_calculusi.pdf

 

You are the best!!!

 

Thank you...

[regentrude]

What I don't always understand though is how far to take an answer.  I might have just left it the way it was.  I don't always know what comes next.  That would help so maybe it'll become clearer to me (eventually). 

 

simplify as far as possible.

How would you have left it?

 

If there's a minus somewhere, see if the quantity is negative and the minus cancels.

If there are double fractions, make it in a simple fraction by inverting the denominator.

If there are factors that can be canceled in numerator and denominator, cancel.

It Terms can be combined, combine.

Rationalize the denominator. 

Split off perfect squares in expressions under a square root and pull out the number. (ex: sqrt (8)= sqrt (4*2)=2 sqrt(2) )

[daijobu]

I remember I always looked forward to the log problems on the AHSME because those were easy points.  There are only 5 logarithm rules, so it's easy to work through them to find the answer.  

 

Also, the log rules are pretty easy to derive in a pinch, using only the relationship between logs and exponents.