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MAThe sine function is one of the most important ideas in trigonometry. It comes from studying right triangles, where sine is the ratio of the side opposite an angle to the hypotenuse. More broadly, sine describes patterns of oscillation, rotation, and wave motion. Its graph is a smooth, repeating curve that goes up and down between –1 and 1, repeating every 360 degrees. Because of this, sine shows up in physics to model things like sound waves, vibrations, and circular motion.
The cosine function is closely related to sine, but instead of the opposite side, it uses the adjacent side over the hypotenuse in a right triangle. Its graph also repeats every 360 degrees and ranges from –1 to 1, but it starts at its maximum value when the angle is zero. This means cosine is like sine shifted to the left by 90 degrees. Together, sine and cosine form a powerful pair for describing cycles, rotations, and harmonic motion. They are used in everything from engineering and computer graphics to analyzing signals and building music synthesizers.
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