# SOHCAHTOA

[soh-kuh-toh-uh]

## What does SOHCAHTOA mean?

SOHCAHTOA is a mnemonic device used to remember the ratios of sine, cosine, and tangent in trigonometry.

## Where does SOHCAHTOA come from?

In the branch of mathematics known as trigonometry, there are three major functions used to determine the angles of right triangles: sine, cosine, and tangent. Relative to the angle one's calculating, each function is found by dividing the lengths of particular sides of the triangle, called the adjacent, opposite, and hypotenuse sides. Sine (S) is calculated by dividing the opposite (O) side over the adjacent (H) side (over referring to the ratio, i.e., opposite/hypotenuse), shortened as SOH. Cosine (C) = adjacent (A)/hypotenuse (H), or COH, and tangent (T) = opposite (O)/adjacent (A), or TOA. All together, these abbreviations form SOHCAHTOA.

SOHCAHTOA, or SOH CAH TOA, appears in print as early as 1944 in trigonometry textbooks as a helpful trick to remember the ratios for students. The mnemonic has since become widespread in math education, sometimes extended in memory-aiding songs or educational stories.

## Who uses SOHCAHTOA?

Many English speakers have remarked on the sound of SOHCAHTOA, comparing it to the names of Native Americans like Sacajawea. One illustration of SOHCAHTOA has featured the right triangle as a mountain and imagines SOHCAHTOA as an American Indian chief. While SOHCAHTOA can be fun to say, as is often noted of the mnemonic, these comparisons can be very insensitive and offensive.

While mostly used by teachers and students in educational contexts often in the 9th grade (ages 14–15) and paired with visual aids, SOHCAHTOA is sometimes used in internet memes, mocking the perceived uselessness of trigonometry in adult life. Other memes use the phrase as the subject of an academic or "nerd" joke, often making trigonometry puns using the images of real and fictional characters in popular culture.

Some alternative or embellished SOHCAHTOA mnemonics include Tommy On A Ship Of His Caught A Herring (perhaps better known in the UK), Studying Our Homework Can Always Help To Obtain Achievement, and Some Old Hippy Caught Another Hippy Tripping On Acid.

## For example

I'm only just learning areas of shapes...the hells Ajacent? Hypotenuse? Sohcahtoa? They all sound like lyrics to Big Shaq's next song "Not So Quick Maths"

‏@TheyCallMeChips, March, 2018

Students will be familiar with the mnemonic SOHCAHTOA, which explains trig formulas -- sine opposite hypotenuse, cosine adjacent hypotenuse and tangent opposite adjacent -- the formulas needed to solve the side/angle relationships of right triangles.

Hope Babowice, Daily Herald, January, 2016

At age 12 she was more lonely than ever. She knew it was time to select her grown name. She decided on a name that held the secret to all of her trigon findings in its spelling. Her sincere desire was that someday she would meet a person who would hear her name and understand the code. She would only be safe with someone who was able to understand her name...She picked Soh-Cah-Toa.

S.K. Martz, The Math Lab, 2001