How to Remember the Ratios for the Three Basic Trig Functions

By Mary Jane Sterling

The legend of SohCahToa is an easy way to remember the ratios for the three basic trig functions. Sure, the story is pretty lame, but you’ll find it very useful when trying to remember the ratios for the three basic trig functions:

  • Soh stands for Sine Opposite Hypotenuse.

  • Cah stands for Cosine Adjacent Hypotenuse.

  • Toa stands for Tangent Opposite Adjacent.

And now, for the fun part: the legend of an Indian chief named SohCahToa (read that: soak-uh-toe-uh). Many years ago, a tribe of American Indians lived along the Illinois River, where they hunted and fished and did what was necessary to live in peace. One young brave was trying to learn to use his bow and arrows effectively, and he was having all sorts of trouble.

Out of frustration, he kicked what he thought was something soft, but it was a rock. His toe turned blue and throbbed all day and night. He tried wrapping it, rubbing it, and ignoring it, but nothing gave him any relief. His mother, a wise squaw, finally had enough of his complaining and said, “Go down to the river, now, and Soh Cah Toa!”

The young brave went to the river, put his toe in the cool water, and got relief. He never did get proficient with the bow and arrow, and he kept kicking things in frustration. Pretty soon, he was known as SohCahToa.

People who studied trigonometry in the past may not remember too many details about it, but one thing they do remember is SohCahToa, if they’ve heard the story (or something similar).