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Math Mnemonics and Songs for Trigonometry

Related Topics: More Math Mnemonics


A collection of math mnemonics for trigonometry - memory aids for various math facts and figures.

In this lesson, we will have mnemonics and songs to help you remember

  • trigonometric ratios for right triangles - SOHCAHTOA
  • reciprocal trigonometric functions - cosecant, secant, cotangent
  • the signs of trigonometric ratios for each quadrant - ASTC or CAST
  • the values on the unit circle
  • Trig Values for Special Angles
  • Pythagorean Identities


Trigonometric Function Definitions

• Remember SOH-CAH-TOA

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tangent = Opposite/Adjacent

SOHCAHTOA, and how use you can use SOHCAHTOA to help you remember the right triangle definitions of the trig functions, assuming that you can remember to spell SOHCAHTOA. A SOH-CAH-TOA song to help you remember. This video lesson explains trigonometry through song. It explains Hypotenuse, Opposite and adjacent and how to use SOHCAHTOA

A SOH-CAH-TOA mnemonic: Some Old Horses Can Always Hear Their Owner’s Approach

• Oscar/Had (sin) A/Heap (cos) Of/Apples (tan)

The Old Arab Carried A Heavy Sack Of Hay
Tan = Opp/Adj; Cos= Adj/Hyp; Sin= Opp/Hyp

Reciprocal Trigonometric Functions

Cosecant = 1/sine
Secant = 1/cosine
Cotangent = 1/tangent
Mnemonic for Reciprocal Trig Functions.

Function Properties

ASTC (Where are they positive?)

Which trig functions are positive in each quadrant:

All in Quadrant I,

Sine in Quadrant II,

Tangent in Quadrant III,

Cosine in Quadrant IV.

Mnemonics include “A Smart Trig Class”, “All Students Take Calculus”, “All Stores Take Cash”, and “Aunt Sally Tickles Cobras” (Cats, Camels, Cougars, Chimps, Caribou ...)

This video demonstrates the ASTC rule used to determine the sign of the trigonometric function in each quadrant. CAST Rule

We can use a mnemonic like CAST or ASTC - All Students Take Calculus to remember the signs in the 4 quadrants.

cast rule for trigonometry

The CAST Rule is a mnemonic device to help remember how the sign of the primary trigonometric ratios is connected to the quadrant that contains the terminal arm of the angle. We use the CAST Rule, principal angles, the special triangles, and SOHCAHTOA to calculate trigonometric ratios

Unit Circle

A way to remember the Entire Unit Circle for Trigonometry. A song to help you remember the unit circle. Trig Values for Special Angles

sin cos tan 30, 45, 60, 90
Simple Hand Trick for Memorizing Trig Values of Special Angles

How to Memorize Pythagorean Identities Easily
Memorize the Pythagorean Trigonometric Identities by creating a story you can use to recall the identities whenever you need them.
sin2 θ + cos2 θ = 1
tan2 θ + 1 = sec2 θ
cot2 θ + 1 = csc2 θ

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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