unit circle quadrants all students take calculus

Quadrant II (angles from 90 to 180 degrees, or π/2 to π radians): Sine and cosecant functions are positive in this quadrant.

Quadrant I (angles from 0 to 90 degrees, or 0 to π/2 radians): All trigonometric functions are positive in this quadrant.

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. Signs of trigonometric functions in each quadrant.Īll Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. Longer mnemonics for these letters include 'Oscar Has A Hold On Angie' and 'Oscar Had A Heap of Apples.' All Students Take Calculus Īn alternate way to remember the letters for Sin, Cos, and Tan is to memorize the nonsense syllables Oh, Ah, Oh-Ah (i.e.

Communities in Chinese circles may choose to remember it as TOA-CAH-SOH, which also means 'big-footed woman' ( Chinese: 大腳嫂 Pe̍h-ōe-jī: tōa-kha-só) in Hokkien. 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). Phrases Īnother 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'. ˌ s oʊ k ə ˈ t oʊ ə/ SOH-kə- TOH-ə, similar to Krakatoa). One way to remember the letters is to sound them out phonetically (i.e.

Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent 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: Image mnemonic to help remember the ratios of sides of a right triangle

Unit circle quadrants all students take calculus