# Edit Edit an Image Page: Waves

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Image Title*: This main image is called "Flame." :This image shows the graph of \sin(x \cdot \sin y)=\cos(y \cdot \cos x)\,. It is the composition of complicated sinusoidal waves. '''Wave Mathematics - [[Basic Trigonometric Functions|Trigonometric Functions]]''': Waves are familiar to us from the ocean, the study of sound, earthquakes, and other natural phenomena. But as any surfer can tell you, ocean waves come in very different sizes, as can all waves. To fully understand waves, we need to understand measurements associated with these waves, such as frequency, wavelength, and amplitude. While these measurements help describe waves, they do not help us make predictions about wave behavior. In order to do that, we need to look at waves more abstractly, which we can do using a mathematical formula. It is possible to look at waves mathematically because a wave's shape repeats itself over a consistent interval of time and distance. This behavior mirrors the repetition of the circle. Imagine drawing a circle on a piece of paper. Now imagine drawing that same shape while your friend slowly pulled the piece of paper out from under your pencil - the line you would have drawn traces out the shape of a wave. One rotation around the circle completes one cycle of rising and falling in the wave, as seen in the picture below. [[image:SinusoidGen.png|cycle|thumb|center|400px]] Mathematicians use the sine function ([[Basic Trigonometric Functions|Sine]]) to express the shape of a wave. The mathematical equation representing the simplest wave looks like this:
y=\sin x