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Understanding Exact Trigonometric Ratios

Trigonometry is a vital branch of mathematics that deals with the relationships between the angles and sides of triangles. Among its many applications, the understanding of exact trigonometric ratios for specific angles is fundamental. This article explores the exact ratios for sine, cosine, and tangent for five key angles measured in radians: (0), (\frac{\pi}{6}), (\frac{\pi}{4}), (\frac{\pi}{3}), and (\frac{\pi}{2}).

Basics of Radians and Degree Conversion

Before diving into the calculations, it's essential to recognize that trigonometric angles can be measured in both degrees and radians. The angles discussed here correspond to the following degree measures:

(0) radians = (0^\circ)