Tangent

Tangent is the periodic trigonometric function defined by tan(x) = sin(x)/cos(x) wherever cosine is nonzero. It has period π, vertical asymptotes at odd multiples of π/2, and zeros at integer multiples of π.

Sine: Sine is a periodic trigonometric function that gives the vertical coordinate of a unit-circle point at a given angle. Tangent uses sine as its numerator.
Angle: An angle measures the rotation or separation between two rays sharing an endpoint. Tangent takes an angle as its input.
Slope: Slope measures a line’s vertical change divided by its horizontal change. A line making angle θ with the horizontal has slope tan(θ).
Cotangent: Cotangent is the trigonometric function cos(x)/sin(x), defined where sine is nonzero. It is the reciprocal of tangent wherever both functions are defined.
Special angles: Special angles are standard angles, such as 30°, 45°, and 60°, whose trigonometric values are exact and simple. Their tangent values follow directly from unit-circle coordinates.
Cosine: Cosine is a periodic trigonometric function that gives the horizontal coordinate of a unit-circle point at a given angle. Its zeros create tangent’s vertical asymptotes.
Radian: A radian is an angle unit equal to the central angle subtended by an arc whose length equals the circle’s radius. Tangent’s period and standard values are commonly expressed in radians.
Inverse trigonometric functions: Inverse trigonometric functions return angles from trigonometric-function values, with restricted domains chosen to make them single-valued. The inverse tangent recovers an angle from a slope or ratio.
Secant: Secant is the trigonometric function 1/cos(x), defined where cosine is nonzero. It shares tangent’s excluded inputs but measures a reciprocal cosine instead.
Tangent of 45 degrees: The tangent of 45 degrees is 1, since sine and cosine are equal at that angle. This exact value corresponds to a line of slope one.

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