The Inverse Tangent Function: Definition, Range, And Applications

Tan^-1(x)

1/1+x^2

The notation tan^-1(x) represents the inverse tangent function. In other words, tan^-1(x) gives us the angle theta (in radians) whose tangent is x.

The domain of the inverse tangent function is all real numbers. However, the range of the inverse tangent function is restricted to the interval (-π/2, π/2). This means that the output of the inverse tangent function will always be an angle between -π/2 and π/2.

For example, if we want to find the angle whose tangent is 1, we can write:
tan^-1(1) = π/4 radians, or 45 degrees.

Similarly, if we want to find the angle whose tangent is -0.5, we can write:
tan^-1(-0.5) = -0.464 radians, or -26.57 degrees.

It is important to note that the inverse tangent function is just one of the inverse trigonometric functions, along with the inverse sine and inverse cosine functions. These functions are useful in a variety of applications in mathematics, physics, and engineering.

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