Cosine Function
f(x) = cos x
The cosine function is a mathematical function that is commonly used in trigonometry. It is denoted by the symbol cos and is defined as the ratio of the adjacent side of a right-angle triangle to its hypotenuse.
In other words, if we have a right-angled triangle with an angle θ, then cos θ is equal to the length of the adjacent side divided by the length of the hypotenuse. This can be represented mathematically as:
cos θ = adjacent side / hypotenuse
The cosine function is a periodic function that oscillates between the values of -1 and 1. Its period is 2π, meaning that it repeats itself every 2π units of angle. Its graph is a wave-like curve that starts at 1, reaches 0 at π/2, goes to -1 at π, returns to 0 at 3π/2 and again reaches 1 at 2π.
The cosine function has several applications in mathematics and physics, such as in signal processing, Fourier analysis, wave propagation, and vibration analysis. It is also used in many real-life scenarios, such as calculating the angles and distances between objects, determining the position and orientation of objects in space, and in navigation systems.
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