- #1
ianbell
- 20
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Does the function f(x) = x tan(x) have a name? I am particularly interested in the solutions to x tan(x) = k for integer k. Do these numbers have an accepted name or notation?
TIA.
TIA.
arildno said:In other words, you are free to invent your own names.
The equation for X tan(x) is simply x tan(x), where x is the variable and tan(x) represents the tangent function.
The inverse of X tan(x) is arctan(x), also known as the inverse tangent function. This means that arctan(x) will "undo" the effect of X tan(x) and return the original value of x.
The domain of X tan(x) is all real numbers except for values where tan(x) is undefined, which occurs at every odd multiple of π/2 (e.g. π/2, 3π/2, 5π/2, etc.).
The range of X tan(x) is all real numbers. However, since the tangent function has vertical asymptotes at every odd multiple of π/2, the range will have gaps at these points.
X tan(x) is used in a variety of fields, including physics, engineering, and economics. It is commonly used to model oscillations, such as the motion of a pendulum or the voltage fluctuations in an AC circuit. It is also used in trigonometric identities and in solving various mathematical problems.