Definition: The word "arctangent" comes from the Latin for "angle tangent." It's a trigonometric function that measures an angle in relation to its nearest right angle or the adjacent side to it. Definition: - The arctangent function, denoted by tan^(-1), is the inverse of the tangent function. It returns the angle whose sine is given by the tangent. This formula defines tan^(-1)(x) = (arctan(x)) in terms of radians: arctan(x) = tan^-1(x) - The arctangent has a period of π/2 and can be extended to any whole number radian or degree value by restricting the argument x. For example, if we have an angle θ (in degrees), we can calculate its arctangent as: tan^(-1)(θ) = (arctan(θ)) in radians tan^(-1)(θ) ≈ 53.11° - The arctangent of a number lies on the unit circle, with angles π/2 to 3π/2 radians indicating right angles and π to 4π radians indicating circles. Here are some other trigonometric functions: - Cotangent (cos^-1): tan^(-1)(x) ≈ cot^-1(x) cot^(-1)(x) = arctan(x) - Sine: sin(θ) = cos(90° - θ) sin(θ) ≈ 0.8457 sin(π/6) ≈ 0.8457 - Cosine: cos(θ) = tan(θ) cos(θ) ≈ 1 cos(90° - θ) ≈ 0 cos(π/2) ≈ 0 - Tangent (tan(x)): tan^(-1)(x) ≈ tan^-1(x) tan^(-1)(x) ≈ 37.58° tan(π) ≈ 0 Arctangent is a special kind of tangent, which returns the angle corresponding to the reciprocal of the sine value.

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