Mnemonics in trigonometry

In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions.

The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English:

One way to remember the letters is to sound them out phonetically (i.e. /ˌsoʊkəˈtoʊə/ SOH-kə-TOH-ə, similar to Krakatoa).

Another method is to expand the letters into a sentence, such as "Some Old Horses Chew Apples Happily Throughout Old Age", "Some Old Hippy Caught Another Hippy Tripping On Acid", or "Studying Our Homework Can Always Help To Obtain Achievement". The order may be switched, as in "Tommy On A Ship Of His Caught A Herring" (tangent, sine, cosine) or "The Old Army Colonel And His Son Often Hiccup" (tangent, cosine, sine) or "Come And Have Some Oranges Help To Overcome Amnesia" (cosine, sine, tangent). Communities in Chinese circles may choose to remember it as TOA-CAH-SOH, which also means 'big-footed aunt' (Chinese: 大腳嫂; Pe̍h-ōe-jī: tōa-kha-só) in Hokkien.^{[citation needed]}

An alternate way to remember the letters for Sin, Cos, and Tan is to memorize the syllables Oh, Ah, Oh-Ah (i.e. /oʊ ə ˈoʊ.ə/) for O/H, A/H, O/A. Longer mnemonics for these letters include "Oscar Has A Hold On Angie" and "Oscar Had A Heap of Apples."

All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.

Other mnemonics include:

Other easy-to-remember mnemonics are the ACTS and CAST laws. These have the disadvantages of not going sequentially from quadrants 1 to 4 and not reinforcing the numbering convention of the quadrants.