Mnemonics in trigonometry
In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions. SOH-CAH-TOA. 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. , similar to Krakatoa). Phrases. 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). Communities in Chinese circles may choose to remember it as TOA-CAH-SOH, which also means 'big-footed woman' () in Hokkien. An alternate way to remember the letters for Sin, Cos, and Tan is to memorize the nonsense syllables Oh, Ah, Oh-Ah (i.e. ) 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." Fractional Form. Another way to remember all the reciprocal trigonometric function, including Cosecant, Secant and Cotangent, is use the following "fraction": Remember the phrase this way - OAOHHA. Starting left to right, then top to bottom, Sine = O/H, Cosine = A/H and Tangent = O/A. To get the reciprocals, then go from bottom up - Cosecant = H/O, etc. All Students Take Calculus. 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. Sines and cosines of special angles. Sines and cosines of common angles 0°, 30°, 45°, 60° and 90° follow the pattern formula_2 with for sine and for cosine, respectively: Hexagon chart. Another mnemonic permits  all of the basic identities to be read off quickly. The hexagonal chart can be constructed with a little thought: Starting at any vertex of the resulting hexagon: Aside from the last bullet, the specific values for each identity are summarized in this table: