What Are the Characteristics of Graphs of Sine and Cosine Functions?

We can use these functions to model a number of different phenomena like sound and light. There are a ton of different applications for these functions, the most interesting one that I heard of lately is creating predictive weather modelling. A series of climate scientists have built an algorithm that simply is feed data from 9 different weather stations, and it predicts the weather for the next 5 days with 87% accuracy. That 13% of inaccuracy is due to the limitations of the equipment that is monitoring the conditions of nature. The model works by reflecting a graph of these functions.

The sine and cosine function relate numeric values to points of the unit circle. With this in mind, we can imagine what those values would look like when they are plotted on the cartesian plane. If you were to consider the sine function, the x variable is the input value for the function while still maintaining a horizontal position on the angle. The y variable would be the output of the function and represent the vertical position on the angle. We can then take these values and plot them in a continuous manner to visualize this function. You can do the same thing with cosine function.

Because of the manner in which functions relate to the unit circle, they do often give off distinct shapes when they are plotted on a graph. They will often form waves in horizontal direction. They characteristically look like a snake moving up and down. We often will make sense of these waves by measuring the distance between each wave and the height or descent of the individual waves. The height is commonly referred to as the amplitude. The greater the value, the taller the wave. The graphs that they form are reflective and often continuous.