Trigonometry mnemonics
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.
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Mnemonics for recalling the definitions of sine, cosine and tangent
Mnemonics with explicit sine, cosine and tangent
These mnemonics take the first letters of
- Sine = Opposite/Hypotenuse
- Cosine = Adjacent/Hypotenuse
- Tangent = Opposite/Adjacent
and form some easily-remembered sentence. Popular examples are
- Some Old Horses Chase And Hunt Till Old Age
- Some Old Hippie Caught A High Tripping On Acid
- Signs Of Happiness Come After Having Tubs Of Acid
- Some Old Hags Can't Always Hide Their Old Age
- Some Old Horses Can Always Hear Their Owner's Approach
- Silly Old Harry Caught A Herring Trawling Off America
- Silly Old Hippies Can Always Have Tonnes Of Acid
- Some Old Hippie/Hippy Came Around Here Tripping On Acid (or "...Caught Another Hippie...")
- SOHCAHTOA (sounds like "soak a toe-a", can be read as "soccer tour")
Mnemonics with implicit sine, cosine and tangent
These mnemonics do not include the function name. Each pair of words implicitly refers to sine, cosine, and tangent respectively. The first letters of
- Opposite/Hypotenuse (=Sine)
- Adjacent/Hypotenuse (=Cosine)
- Opposite/Adjacent (=Tangent)
are used to form a sentence. Popular examples are
- Old Houses Always Have Old Attics
- Oh Heck, Another Hour Of Algebra!
- Oscar Had A Hit Of Acid
- Old Hippies Are High On Acid
- Oscar Has A Heap Of Acorns
- Orla Has A Hell Of A...
Mnemonics for recalling which functions are positive in which quadrant
These mnemonics help recall which functions are positive in which quadrant, starting at the conventional 0 (east on a compass) and going counter-clockwise. They take the first letters of
- All functions are positive in quadrant I
- Sine is positive in quadrant II
- Tangent is positive in quadrant III
- Cosine is positive in quadrant IV
and form a simple sentence. Popular examples are
- All Students Take Calculus
- A Simple Trig Chart
- All Stations To Central
- All Sinners Take Confession
- All Science Teachers Care
- Another Stupid Trig Class
- All Students Talk Crap
Other mnemonics
These mnemonics define the same functions as above, but in a different order. Popular examples are
- Old Harry Spills All His Custard Over Auntie's Tablecloth
- Old Harry Spills: Opposite/Hypotenuse = Sine
- All His Custard: Adjacent/Hypotenuse = Cosine
- Over Auntie's Tablecloth: Opposite/Adjacent = Tangent
- Oly And Olivia Have Hairy Ankles (defines Sine | Cosine | Tangent as follows)
- Oly And Olivia: Opposite | Adjacent | Opposite
- Have Hairy Ankles: Hypotenuse | Hypotenuse | Adjacent
- Sally Can Tell Oscar Has A Hat On Always
- Sally Can Tell: Sine, Cosine, Tangent
- Oscar Has: Opposite/Hypotenuse (=Sine)
- A Hat: Adjacent/Hypotenuse (=Cosine)
- On Always: Opposite/Adjacent (=Tangent)