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Sine - Monomath Math Dictionary
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Sine

Trigonometry

📖 Definition

Sine is a trigonometric function defined as the ratio of the opposite side to the hypotenuse in a right triangle.

📝 Detailed Explanation

In a right triangle, sin(θ) = opposite/hypotenuse. The sine function ranges from -1 to 1 and is periodic with period 2π (360°). Sine is an odd function: sin(-θ) = -sin(θ). On the unit circle, sin θ gives the y-coordinate. Sine waves describe sound, light, alternating current, tides, and many natural oscillations.

📐 Formula

sin θ = opposite / hypotenuse  |  sin(θ + 2π) = sin θ

📜 History & Origins

Sine originated from the study of chords in Greek astronomy. The Sanskrit word "jya" (bowstring) became "jiba" → "jaib" (cove) in Arabic → "sinus" in Latin. The modern sine function was developed by Indian mathematicians Aryabhata and Madhava, Arabic scholars like Al-Battani, and European mathematicians like Euler.

🔗 Related Terms

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