Math Mnemonics and Songs for Trigonometry
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
Trigonometry
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.
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 C**alculus to remember the signs in the 4 quadrants.
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
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
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