"Sohcahtoa. My Native American friend." These were the words with which the acronym sohcahtoa were first conveyed to me by my high school teacher. "Racism" notwithstanding, I'll never forget it. And it's wildly useful to remember the relationship between sides of a right triangle and the sine, cosine, and tangent of an angle.
You will use these relationships a million times or more in the first two years of physics. This topic will span several episodes, but right now we will concentrate on introducing the sohcahtoa moniker and review some facts about triangles. I highly recommend checking out Episode 027: 27 Triangular Facts and Factoids You Must Know! as a prereq to this, in the event that you're not familiar.
The elements of sohcahtoa, each letter in sohchatoa stands for one of the following:
Sine
Cosine
Tangent
Adjacent
Opposite
Hypotenuse
Of course, sine, cosine and tangent are trigonometric functions and adjacent, opposite, and hypotenuse refer to sides of a right triangle. With this in mind, given any right triangle, we can draw the following three relations of any angle, theta:
In a right triangle, the sides of the triangle can be specified with respect to one of two non-right angles, theta. The hypotenuse is always the longest side, and is the only side which does not form the right angle.
Given an angle theta, the adjacent side is always the side which forms the angle theta with the hypotenuse.
The remaining side, which does not form the angle theta is referred to as the opposite side.
For the other angle, the opposite and adjacent sides are reversed.
