A mnemonic for the trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Sohcahtoa is a memory trick that helps students recall the three basic trigonometric ratios used in right triangles. Each syllable stands for a ratio and the two sides used to calculate it.
Breaking it down:
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SOH: Sine = Opposite ÷ Hypotenuse
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CAH: Cosine = Adjacent ÷ Hypotenuse
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TOA: Tangent = Opposite ÷ Adjacent
In a right triangle, the hypotenuse is always the longest side, opposite the right angle. The opposite side is across from the angle being used, and the adjacent side is next to that angle (but isn't the hypotenuse).
For example, if a right triangle has an angle θ, an opposite side of 3, an adjacent side of 4, and a hypotenuse of 5:
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sin(θ) = 3/5
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cos(θ) = 4/5
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tan(θ) = 3/4
Sohcahtoa doesn't teach a new concept on its own. It's a shortcut for remembering which sides go where once the three trig ratios have already been introduced.
When Do Students Learn About Sohcahtoa?
Students learn Sohcahtoa once they begin formal work with right triangles and trigonometry.
Grades 6–8 – Right Triangles and the Pythagorean Theorem
Students study the parts of a right triangle and the relationships between its sides, laying the groundwork for trigonometric ratios.
Grades 9+ – Trigonometric Ratios
Students learn sine, cosine, and tangent formally, using Sohcahtoa to organize and recall the three ratios when solving right triangle problems.
