What is trigonometry?
Answers
Taking apart the roots of the word, trigonometry is the measurement of triangles. And that's actually a pretty accurate definition. Thing is, triangles are EVERYWHERE, They are the simplest polygon you can think of, so if you learn everything you can about triangles, you can say a lot about geometry in general. You can make a hexagon out of six triangles for example. And studying a triangle is a lot easier than studying hexagons. You might have heard someone in a movie say that they are going to "triangulate" the position of something. The reason they can do that is that with almost any two angles opening toward each other some known distance apart, you've got a triangle that you can know all of the dimensions of though trigonometry. You could, conceivably hexagonalate a position too, but that would be needlessly complicated and redundant.
Aside from helping with problems of geometry, trigonometry also helps us understand periodic movements. If you think of the second hand of a clock, you might imagine it starting out at the 3 o'clock position, and then moving down to the 6 o'clock position. In that time the second hand will have covered an angle of 90 degrees. If you draw an imaginary line connecting the tip of the hand at the three o'clock position with the point where the tip of the hand is at the three o'clock position, you will have a concept of a triangle of time, as opposed to space. You can make triangles between any two times, and you can start to notice patterns between the lengths of the sides of the triangle at any given moment. From here you can generate what's called a sine wave function. And functions like these can describe any periodic movement you can think of, from the movement of a spring to the sound waves of your voice as you speak into a telephone receiver.