# SOHCAHTOA

## or SOH-CAH-TOA or SOH CAH TOA

[soh-k*uh-***toh**-*uh*]

##### Examples of SOHCAHTOA

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##### Examples of SOHCAHTOA

*The Math Lab*,

*2001*

## 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.*