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. A mnemonic (AmE [] or BrE []) is a memory aid. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...

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

A war cry Soh Cah Toa

• Some Officers Have Coaches And Horses To Order Around
• Some Old Horses Chase And Hunt Till Old Age
• Some Old Hippie Caught A High Tripping On Acid
• Some old Hippe Caught Another Hippie Tripping on Acid
• Signs Of Happiness Come After Having Tubs Of Acid
• Some Old Hags Can't Always Hide Their Old Age
• Some Old Hobos 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")
• Silly Old Hitler Chased A Horse Through Our Attic
• Silly Old Hitler Caused Awful Headaches To Our Airmen
• Sir Olivers Horse Came Ambling Home to Olivers Aunt
• Some Old Hag Cracked All Her Teeth On Asparagus
• Some Orifices Have Curly Auburn Hair To Obscure Approach (RAF mnemonic from WW2)
• Saddle Our Horses Canter Away Happily To Other Adventures
• See Old Harry Catch A Herring Trawling Off America
• The Old Aunt Sat On Her Coat And Hat
• Selly Oak Hospital Can Always Help The Odd Accident
• SAKATA from the television advert.

Perhaps a somewhat stranger memory trick involves imagining that you are throwing a bucket of water at the tower of London, in which The Queen is currently residing. She responds to the water by saying:"Hey, Phil, someone's trying to Soak Our Tower!". Because of The Queen's more formal accent, it sounds more like SOH CAH TOA.(So kar to-a). As daft as it sounds, the bizzareness of it should help you to remember it.

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
• Oscar Had A Hunk Of A..
• Oscar Has A Heap Of Apples
• Orla Has A Hell Of A...
• One Hopes And Hopes On America

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 Silver Tea Cups
• All Students Take Calculus
• All Students Take Cocaine
• A Simple Trig Chart
• All Stations To Central
• All Stations To Crewe
• All Sinners Take Confession
• All Science Teachers Care
• All Students Take Chemistry
• Another Stupid Trig Class
• All Socialists Talk Crap
• Albany State Teachers' College
• Add Sugar To Coffee
• All Smackheads Take Crack

The University at Albany, (formerly known as Albany State University until the early 1990s) located in Albany, New York, in the USA, is one fo four university centers of the State University of New York. ...

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

• Oranges Have Sections and Apples Have Cores.

Oranges Have: Opposite/Hypotenuse (=Sine)

Apples Have: Adjacent/Hypotenuse (=Cosine)

• 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)

• The Cat Sat On An Orange And Howled Horribly

The Cat Sat: Tangent, Cosine, Sine

On An Orange: Opposite, Adjacent, Hypotenuse (=top of each ratio)

And Howled Horribly: Adjacent, Hypotenuse, Hypotenuse (=bottom of each ratio)

This is meant to be read vertically, in columns.

Another mnemonic uses rhythm to help students remember the sine and cosine of the sum of two angles. In mathematics, trigonometric identities (or trig identities for short) are equations involving trigonometric functions that are true for all values of the occurring variables. ...

• Sin Sin Co Co Sin: Sin(A + B) = Sin(A)Cos(B) + Cos(A)Sin(B)
• Co Co Co Sin Sin: Cos(A + B) = Cos(A)Cos(B) - Sin(A)Sin(B)