Cosine

Cosine is a periodic function that gives the horizontal coordinate of a point moving around the unit circle. It also relates the sides and angles of right triangles.

Unit circle: The circle of radius one centered at the origin of a coordinate plane. Cosine is the horizontal coordinate of the point on this circle.
Cosine addition formula: The identity expressing cosine of a sum as a combination of sines and cosines. It derives cosine values for combined angles from values at each angle.
Law of cosines: A triangle identity relating one side’s length to the other sides and their included angle. It extends the Pythagorean theorem by using the cosine of a triangle angle.
Tangent: The trigonometric function sin x divided by cos x, defined where cosine is nonzero. Unlike cosine, tangent has vertical asymptotes and is not defined at every angle.
Angle: A measure of rotation or separation between two rays sharing an endpoint. Cosine takes an angle as its input.
Euler's formula: The identity connecting the complex exponential to sine and cosine: e^(ix) = cos x + i sin x. It packages cosine and sine into one expression using complex numbers.
Dot product: An operation on vectors equal to the product of their lengths and the cosine of their angle. It uses cosine to measure directional alignment between vectors.
Inverse cosine: The function arccos that returns an angle in [0, π] for a cosine value in [−1, 1]. It reverses cosine only on a restricted interval where cosine is one-to-one.
Radians: A unit of angle measure defined by the ratio of arc length to radius. Radians make cosine’s input align directly with motion around the unit circle.
Derivative of cosine: The derivative of cos x, equal to −sin x. It describes cosine’s instantaneous rate of change.

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