How do Sine Cosine and Tangent work?

Answer 1

Sine, cosine, and tangent all assume you have a right triangle (where one angle is 90 degrees). Each function operates on one number, which represents another angle (call it x) in the triangle. We write these functions as sin(x), cos(x), and tan(x).

Now, we're going to give names to each of the 3 sides. The longest side (the one not touching the right angle) is the hypotenuse. The side touching our angle x, but not the hypotenuse, is the adjacent side. The left-over side is the only one not touching our angle x, which we call the opposite side. We call the length of the hypotenuse h, the length of the adjacent side a, and the length of the opposite side o.

Then sin(x)=o/h

cos(x)=a/h

tan(x)=o/a.

People use the made-up word "sohcahtoa" ("SOAK-a-TOE-ah") to remember this. each third of the word stands for a different function: the letters "soh" stand for "sine" is "opposite" over "hypotenuse", and similarly for "cah" and "toa".