I always show my geometry students the old trig mnemonic "Some Of Her Children Are Having Trouble Over Algebra" (sin A = opp/hyp; cosA = adj/hyp; ten A = opp/adj). Then I ask them to construct their own mnemonics. The next day, I collect the mnemonics and read the interesting ones to the class. The following are my favorites.
SOHCAHTOA!
1. So often have cruel and hateful tricks opened arguments.
—Sam Feikema, 1991
2. Some out-houses can actually have totally odorless aromas.
—Michael Gibson, 1989
3. She offered her cat a heaping teaspoon of acid.
—Allison Morgan, 1991
4. Shoplifting often happens. Cathy admitted her theft one afternoon.
—Guilia Perazzoli, 1980
5. Stueben owes his class a hardy ton of A's. —Stephanie Deller, 1980
6. Stueben's original homework causes awful headaches to over-achievers.
—Becky Beasley, 1989
7. Soaring over Haiti, courageous Amelia hit the ocean and . . .
—Lisa Wakeham, 1980
8. Stamp out homework carefully, as having teachers omit assignments.
—Stephanie Deller, 1980.
9. School! Oh how can anyone have trouble over academics.
—David McCulloch, 1980.
10. Some of her children are having trouble over algebra.
—Anonymous, pre-1968
11. Smart Children Think: Oscar had a heap of apples. Or (to the tune of Yankee Doodle Dandy) Oscar had a heap of apples, sine and cosine tangent.
—Anonymous
12. Sing out happily, 'cuz a healthy tune obtains applause.
—Andrea Agostini, 1989
13. Students often hardly concentrate after hearing the only answer.
14. Sin—oh! Cos—ah! Tan—oh/ah! —T. Percy Nunn, 1928 Oh heck! Another hour of algebra with some crazy teacher.
—Dictionary of Mnemonics, 1972
16. Sine-off helps congestion and headaches. Take one anyway.
—J.B. Wilson, 1980
15.
—Andrea Agostini, 1989
In which quadrants do the six trig functions take positive values? Figure 14 provides the answer, but how shall we remember it?
| S | A |
| T | C |
A = All Functions
S = Sine only
T = Tangent only
C = Cosine only
FIGURE 1 4
Starting in the first quadrant and proceeding counterclockwise (like an angle going from 0° to 360°), we say: All Students Take Calculus or Awful Stinky Trig Course or Are Simpletons Teaching Courses? or Are Schools TestCrazy? or All Schools Torture Children. Since a function and its reciprocal have the same sign, the letters ASTC (or the ACTS mnemonic or the iron CAST rule) also indicate the signs in the different quadrants of the cosecant, secant, and cotangent.
Sin (t)
+1
0 0
-1
Cos (t)
0
-1 +1
0
FIGURE 1 5
Notice that the middle letter of sin is i (looks like 1) and the middle letter of cos is o (looks like zero). If we place these words above the positive Taxis, then these diagrams become easier to memorize (see Figure 15). Another curious mnemonic is this chart:
~ 0° 30° 45° 60° 90°
What are the radian values of the standard angles 120°, 135°, and 150°? Answer: Take the middle digit, divide by the following consecutive digit, and append fir: 2~r/3, 3;r/4, 5;r/6. (Thanks to C. B. Brown, my former precalculus student.)
