Math. I loves me some math.
Hello, South Korea!
Howdy, Poland! Or is that Indonesia in trouble?
(Flag humor. Ha ha!)
I like this picture. It gives you all the trig functions as lengths of line segments. The square OBCF has sides that are all length 1, and the line segment OH is also length 1, because H is on the unit circle with center at O. The variable alpha is the length of the arc of the circle from F to H. When we do trig, we measure angles in radians, which is to say distances of parts of the circle, so all the way around the circle is 2 times pi instead of 360 degrees. The lengths of line segments OG and OA are cosine and sine, respectively. Any text book will show that. But the line segments for tangent, cotangent, secant and cosecant aren't shown as often. I think it's a good aid for visual learners. Why this works for any angle where cosine times sine doesn't equal zero is similar triangles.
Then we have the quadratic formula, a different topic completely. Trig is about lines and the unit circle, the quadratic is about parabolas of any size and the x-axis. Here, the problem is memorization. The best trick for memorization is a tune. Catchy tunes, what commenter Fran calls earworms, get stuck in your head forever. Anyone old enough to remember Plop, plop, fizz, fizz, Oh what a relief it is now has that tune stuck in their head for the rest of the day.
Please, don't bother thanking me.
For the quadratic, let's use a much older earworm that everybody knows, Pop Goes The Weasel. These words don't rhyme, but when you think of it, neither do the original lyrics to Pop Goes The Weasel, unless you say weasel rhymes with weasel, which I think is a pretty weak argument.
DaDa DaDa dadadaDum (da)
DaDa DaDa daDaaDa (da)
DaDa DaDa dadadaDum
Dum DaDa DaaDum
The da in parentheses at the end of the first and second lines is the stolen beat for the "the" in front of monkey in the next line. Sing it; you'll know what I mean. I put them in parentheses to help the lyric to scan.
X-will e-qual ne-ga-tive-B (with)
Plus-or mi-nus the-square-root (of)
B-squared mi-nus 4-times-A-C
All o-ver 2-A.
Sing this three times. The quadratic formula will then be stuck in your head until your death bed.
Now I will accept your thanks, on behalf of a grateful nation.
p.s. I have a new post on The Smirking Chimp, about rhetorical questions. No math involved, I promise. Not even any catchy tunes