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Unit Circle Trig Definitions Definition

Unit circle trig definitions are a set of definitions of the trigonometric functions sine, cosine, tangent, cosecant, secant, and cotangent all of which are derived from the unit circle. The unit circle plays a significant role in several different areas of mathematics. In particular the functions of trigonometry are most simply defined using the unit circle. As shown in the figure below, a point p on the terminal side of an angle θ in angle standard position measured along an arc of the unit circle has as its coordinates (cos θ, sin θ) so that cos θ is the horizontal coordinate of p and sin θ is its vertical component. As a result of this definition, the trigonometric functions are periodic with period 2π.

Sources

“Unit Circle.” From Wolfram MathWorld, mathworld.wolfram.com/UnitCircle.html.

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