Soh-Cah-Toa and Trigonometry Functions

When I was in Trig class, my teacher told us that the single most important figure in the history of Trigonometry was not some mathematician like Blaise Pascal or René DeCartes, but a mythical American Indian chief named Soh-cah-toa. This man’s history and accomplishments are clouded by time, but over the years he has single-handedly helped countless Trigonometry students memorize the formulas for angle functions in a right triangle.

So how did he accomplish this feat, you may ask? Chief Soh-cah-toa’s name is a mnemonic device that will help you remember how to find the sine, cosine, and tangent in a right triangle. Here’s how it works:

Soh

- This is short for Sine equals Opposite side over Hypotenuse. (If you recall, the Opposite side is the side of the triangle directly opposite the angle you’re examining. The hypotenuse is the longest side, the one opposite the right angle.)

Cah

- This is short for Cosine equals Adjacent side over Hypotenuse. (The Adjacent side is the side of the triangle next to the angle you’re examining that is NOT the hypotenuse.)

Toa

- This is short for the Tangent equals the Opposite side over the Adjacent side. (You’ll notice this one doesn’t even need the hypotenuse!)

Chief Soh-cah-toa has helped countless trigonometry students remember basic trig functions. Know his name, and he will help you remember them too.

Get More Help!

Click one of these links to get more help from another Cramlet in this same chapter:

• Soh-Cah-Toa and Trigonometry Functions
• Non-Right Triangles Study Sheet
• Angle Functions Quiz
• My Angle Functions Flashcards
• Tangent & ArcTangent in a Right Triangle
• Tangent Function in a Right Triangle
• Sine & ArcSine in a Right Triangle
• Sine Function in a Right Triangle
• Secant Function in a Right Triangle
• Radians
• Law of Sines Ambiguous Case
• Law of Sines
• Law of Cosines
• Cotangent Function in a Right Triangle
• Cosine & ArcCosine in a Right Triangle
• Cosine Function in a Right Triangle
• Cosecant Function in a Right Triangle
• Area of a Triangle Using Sine