Bill Simmons asks "By the way, can you remember anyone who has ever been Comeback Player of the Year?"
Lee Trevino?
I went into Costco for the first time in... gosh, at least 5 years.
Having heard the good stories about Costco treating its employees better than its investors; and having renewed my interest in cooking, I decided a wander through might be in order.
Costco is really four markets in one:
One stocks items I have no interest in at all.
One stocks items I have use for, but am particular about; right idea, wrong brand.
One stocks items I have use for, but could not possibly consume without a full size freezer and a small swarm of locusts.
One stocks junk food.
So I walked out without restoring my old membership.
I discovered some trig identities this week; as they don't look even a little bit familiar, I assume they didn't come up when I was paying attention in highschool.
In short: for any product consisting of sines and cosines: if there are an odd number of sines, the expression can be rewritten as a sum of sines. If there are an even number of sines, the expression can be rewritten as a sum of cosines.
You can get a quick sense of how this might kind of work out by considering the exponential expression for sign, which has a factor i in the denominator. An odd number of sines in the product produces an odd number of i factors, producing an imaginary number. To get real numbers from this, you'll need to pop one of the i's off again by creating sine terms.
It's all pretty straight forward to do with exponentials and a little bit of induction; or you can demonstrate it using the more common identities....
cos(A)cos(B)
= (1/2) * 2 cos(A)cos(B)
= (1/2) * ( 2 cos(A)cos(B) - sin(A)sin(B) + sin(A)sin(B) )
= (1/2) * ( cos(A)cos(B) - sin(A)sin(B) + cos(A)cos(B) + sin(A)sin(B) )
= (1/2) * ( cos(A)cos(B) - sin(A)sin(B) + cos(A)cos(-B) - sin(A)sin(-B))
= (1/2) * ( cos(A+B) + cos (A-B) )
sin(A)sin(B)
= (1/2) * 2 sin(A)sin(B)
= (1/2) * ( 2 sin(A)sin(B) - cos(A)cos(B) + cos(A)cos(B) )
= (1/2) * ( sin(A)sin(B) - cos(A)cos(B) + cos(A)cos(B) + sin(A)sin(B))
= (1/2) * ( sin(A)sin(B) - cos(A)cos(B) + cos(A)cos(-B) - sin(A)sin(-B))
= (1/2) * ( - (cos(A)cos(B) - sin(A)sin(B)) + (cos(A)cos(-B) - sin(A)sin(-B)))
= (1/2) * ( cos(A-B) - cos(A+B) )
sin(A)cos(B)
= (1/2) * 2 sin(A)cos(B)
= (1/2) * ( 2 * sin(A)cos(B) + cos(A)sin(B) - cos(A)sin(B) )
= (1/2) * ( sin(A)cos(B) + cos(A)sin(B) + sin(A)cos(B) - cos(A)sin(B))
= (1/2) * ( sin(A)cos(B) + cos(A)sin(B) + sin(A)cos(-B) + cos(A)sin(-B))
= (1/2) * (sin(A+B) + sin(A-B))
Roger Ailes pulls a quote from the archives of the Independent Weekly:
When the reorganization took effect on March 1, 2003, [Michael] Brown assured skeptics that under the new arrangement, the country would be served by "FEMA on steroids"--a faster, more effective disaster agency.
So now we have that much more proof of the debilitating effects of steroids - no wonder Congress got all bent out of shape about them.
What's your favorite remedy for habanero burn (i.e. when the capsaicim gets into your skin)?