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A number of mnemonics have been invented by educators to help students remember the rules defining the various trigonometric functions. Some of them are listed here, in no particular order
Some Old Horses Chase And Hunt Till Old Age
- Some Old Horses: sine = opposite/hypotenuse
- Chase And Hunt: cosine = adjacent/hypotenuse
- Till Old Age: tangent = opposite/adjacent
SOHCAHTOA (sounds like "soak a toe-a", can be read as "soccer tour"). It reminds one that:
- SOH: sine = opposite/hypotenuse
- CAH: cosine = adjacent/hypotenuse
- TOA: tangent = opposite/adjacent.
Old Harry Spills All His Custard Over Auntie's Tablecloth. Note that the definition phrasings are the reverse of those in the previous mnemonic.
- Old Harry Spills: opposite/hypotenuse = sine
- All His Custard: adjacent/hypotenuse = cosine
- Over Auntie's Tablecloth: opposite/adjacent = tangent
Oh Heck, Another Hour Of Algebra!. Each pair of words refers implicitly to sine, cosine, and tangent, respectively:
- Oh Heck: sine = opposite/hypotenuse
- Another Hour: cosine = adjacent/hypotenuse
- Of Algebra: tangent = opposite/adjacent
Some Old Hippie Came Around Here Tripping On Acid (or "...Caught Another Hippie...")
- Some Old Hippie: sine = opposite/hypotenuse
- Came Around Here: cosine = adjacent/hypotenuse
- Tripping On Acid: tangent = opposite/adjacent
Sally Can Tell Oscar Has A "Hat" On Always
- Sally Oscar Has: sine = opposite/hypotenuse
- Can A Hat: cosine = adjacent/hypotenuse
- Tell On Always: tangent = opposite/adjacent
Signs Of Happiness Come After Having Tubs Of Acid
- Signs Of Happiness: sine = opposite/hypotenuse
- Come After Having: cosine = adjacent/hypotenuse
- Tubs Of Acid: tangent = opposite/adjacent
Some Old Hags Can't Always Hide Their Old Age
- Some Old Hags: sine = opposite/hypotenuse
- Can't Always Hide: cosine = adjacent/hypotenuse
- Their Old Age: tangent = opposite/adjacent
Some Old Horses Can Always Hear Their Owner's Approach
- Some Old Horses: sine = opposite/hypotenuse
- Can Always Hear: cosine = adjacent/hypotenuse
- Their Owner's Approach: tangent = opposite/adjacent
Silly Old Harry Caught A Herring Trawling Off America
- Silly Old Harry: sine = opposite/hypotenuse
- Caught A Herring: cosine = adjacent/hypotenuse
- Trawling Off America: tangent = opposite/adjacent
Another mnemonic helps recall which functions are positive in which quadrant:
All Students Take Calculus (or a more memorable alternative, referring to any drug starting with 'c'!)
- All = All functions are positive in QI
- Students = Sine is positive in QII
- Take = Tangent is positive in QIII
- Calculus = Cosine is positive in QIV
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