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.

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
• 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

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

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)