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anemone
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Solve the equation $x=\pi\left\lfloor\tan\dfrac{\pi}{x}\right\rfloor$.
anemone said:Solve the equation $x=\pi\left\lfloor\tan\dfrac{\pi}{x}\right\rfloor$.
The floor function, denoted as ⌊x⌋, rounds a given number down to the nearest integer. For example, ⌊3.8⌋ = 3 and ⌊-2.5⌋ = -3.
The floor function is commonly used in mathematical equations and functions to ensure that the resulting value is an integer. It is also used in computer programming to convert floating-point numbers into integers.
The tangent function, usually denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is defined as tan(x) = sin(x)/cos(x).
The domain of the tangent function is all real numbers except for values that make the cosine function equal to 0. In other words, the domain is all real numbers except for x = (2n + 1)π/2, where n is an integer. The range of the tangent function is all real numbers.
The tangent function is used in various fields such as physics, engineering, and architecture. For example, it can be used to calculate the slope of a ramp or the angle of a ladder leaning against a wall. It is also used in navigation and surveying to determine the height of a building or the distance between two points.