All Students Take Calculus

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All Students Take Calculus is a mnemonic in mathematics that is used to help people memorize the sign values of all the trigonometric functions in the 2-dimensional Cartesian coordinate system. The letters ASTC signify which of the trigonometric functions are positive, in the order of the quadrants - starting in the top right quadrant, and moving counterclockwise.

  • In Quadrant I: A for All - all trigonometric functions are positive in this quadrant.
  • In Quadrant II: S for Sine - sine and cosecant functions are positive in this quadrant.
  • In Quadrant III: T for Tangent - tangent and cotangent functions are positive in this quadrant.
  • In Quadrant IV: C for Cosine - cosine and secant functions are positive in this quadrant.

Other variants[edit]

  • Sometimes it is simply referred to as the CAST law, which can be easier to remember than the mnemonics, but one will have to remember that the first quadrant represents All, not Cosine: in other words, that you must start from the IV quadrant.
  • All Stations To Central[1]
  • All Silly Tom Cats[1]
  • Add Sugar To Coffee[1]
  • All Students Take Coffee[1]
  • All Strippers Take Cash
  • All Silver Tea Cups
  • All Science Teachers (are) Crazy

See also[edit]


  1. ^ a b c d "Sine, Cosine and Tangent in Four Quadrants". Archived from the original on 2015-01-18. Retrieved 2015-01-18. 

External links[edit]