cos x
d/dx sin x
In mathematics, cos(x) is the shorthand representation of the cosine function. The cosine function is a trigonometric function that relates the ratio of the adjacent side of a right-angled triangle to the hypotenuse of that triangle.
The cosine function is periodic, with a period of 2π. Therefore, cos(x) has the same value at x, x+2π, x+4π, etc. It is also an even function, which means that cos(-x) equals cos(x) for any value of x.
The values of cos(x) range between -1 and 1. The cosine function attains its maximum value, 1, when x is 0 or any multiple of 2π. Conversely, it attains its minimum value, -1, when x is any odd multiple of π/2 (that is, π/2, 3π/2, 5π/2, etc.).
Some common values of cos(x) include:
– cos(0) = 1
– cos(π/2) = 0
– cos(π) = -1
– cos(3π/2) = 0
– cos(2π) = 1.
The cosine function has many applications in mathematics, physics, engineering, and other fields. It is used to model phenomena that exhibit periodic behavior, such as sound waves, electromagnetic waves, and oscillations in mechanical systems.
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