page_title: Trigonometry
section_title: The unit circle and common trigonometric values
hierarchical_section_title: Trigonometry / Trigonometric ratios / The unit circle and common trigonometric values
context_page_description: Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
  Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.
  Trigonometry is known for its many identities, which are equations used for rewriting trigonometrical expressions to solve equations, to find a more useful expression, or to discover new relationships.
context_section_description: Trigonometric ratios can also be represented using the unit circle, which is the circle of radius 1 centered at the origin in the plane. In this setting, the terminal side of an angle A placed in standard position will intersect the unit circle in a point (x,y), where   and . This representation allows for the calculation of commonly found trigonometric values, such as those in the following table:
caption: Fig. 1a – Sine and cosine of an angle θ defined using the unit circle.
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