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    Sine and cosine - Wikipedia
    In mathematics, sine and cosine are trigonometric functions.

    Sine, Cosine and Tangent - Math is Fun
    Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: Opposite is always opposite the angle. And Adjacent is always next to the angle.

    Sine Core
    Streamline workplace operations with Sine Core, a platform for managing visitors, contractors, and compliance efficiently.

    SINE Definition & Meaning - Merriam-Webster
    The meaning of SINE is the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse.

    Sine by Honeywell - Visitor, Contractor & Compliance Management
    Sine transforms how people move through buildings. Our unified platform connects visitors and contractors to facilities with seamless, secure check-ins, onboarding and on-going compliance.

    Sine Function Calculator | Graph, Values & Formula
    Calculate sine values instantly with our Sine Function Calculator. Enter any angle in degrees or radians for fast, accurate trig results.

    Sine | Definition, Formulas, & Facts | Britannica
    sine, one of the six trigonometric functions, which, in a right triangle ABC, for an angle A, is sin A = length of side opposite angle A/ length of hypotenuse. (The other five trigonometric functions are cosine [cos], tangent [tan], secant [sec], cosecant [csc], and cotangent [cot].)

    Trigonometric functions - Wikipedia
    The sine and cosine functions are one-dimensional projections of uniform circular motion. Trigonometric functions also prove to be useful in the study of general periodic functions.

    Sine Calculator
    Scroll down to understand what is a sine and to find the sine definition, as well as simple examples and the sine graph. Also, you'll find there a simple table with values of sine for basic angles, such as $\mathrm{sin}(0)$, $\mathrm{sin}(30\mathrm{°})$, and many more.

    Sine - Math.net
    Sine, written as sin⁡ (θ), is one of the six fundamental trigonometric functions. There are two main ways in which trigonometric functions are typically discussed: in terms of right triangles and in terms of the unit circle.

     

     

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    Important Trigonometry Terms
    • Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.
    • Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.
    • Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle ($\tan \theta = \frac{\sin \theta}{\cos \theta}$).
    • Cosecant (csc): The reciprocal of the sine function ($\csc \theta = \frac{1}{\sin \theta}$), representing the ratio of the hypotenuse to the opposite side.
    • Secant (sec): The reciprocal of the cosine function ($\sec \theta = \frac{1}{\cos \theta}$), representing the ratio of the hypotenuse to the adjacent side.
    • Cotangent (cot): The reciprocal of the tangent function ($\cot \theta = \frac{1}{\tan \theta}$), representing the ratio of the adjacent side to the opposite side.
    • Hypotenuse: The longest side of a right-angled triangle, located opposite the right angle ($90^\circ$).
    • Radian: A unit of angle measurement based on arc length, where $2\pi \text{ radians} = 360^\circ$ ($1 \text{ radian} \approx 57.3^\circ$).
    • Unit Circle: A circle with a radius of $1$ centered at the origin $(0,0)$ in the Cartesian coordinate plane, used to extend trigonometric functions to any angle.
    • Pythagorean Identity: The fundamental trigonometric identity derived from the Pythagorean theorem, expressed as $\sin^2\theta + \cos^2\theta = 1$.

     

    Industries That Use Trigonometry
    • Architecture & Civil Engineering: Calculates structural loads, roof pitches, bridge support angles, and land slopes to design safe buildings and infrastructure.
    • Aeronautics & Aerospace: Determines flight paths, wind drift angles, satellite orbits, and altitude trajectories for aircraft and spacecraft navigation.
    • Video Game Development & CGI: Renders 3D graphics, calculates character raycasting, models object collisions, and animates realistic movement using vector trigonometry.
    • Land Surveying & Cartography: Measures distances, elevation changes, and geographic boundaries across large areas using triangulation techniques.
    • Acoustics & Audio Engineering: Analyzes sound waves, models frequency harmonics, and designs soundproof spaces using sine and cosine wave functions.
    • Maritime & Ocean Navigation: Computes true heading, compass bearing, ocean current offsets, and celestial navigation coordinates for ships.
    • Electrical & Mechanical Engineering: Models alternating current (AC) voltage waveforms, electromagnetic fields, and rotational forces in motors and machinery.
    • Medical Imaging & Radiography: Reconstructs 3D cross-sectional images in CAT scans and MRI machines by calculating wave projection angles.
    • Astronomy & Astrophysics: Measures interplanetary distances, stellar parallax, and celestial movement relative to Earth.
    • Meteorology & Climate Science: Models global weather patterns, ocean wave dynamics, and solar radiation angles to predict climate and weather systems.
                    

     

     

    Important Trigonometry Historical Events
    • Plimpton 322 Clay Tablet (c. 1800 BC): Records ancient Babylonian mathematical tables containing advanced Pythagorean triples, marking the earliest known use of right-triangle ratios.
    • Hipparchus Compiles First Chord Table (c. 150 BC): Earns the title "Father of Trigonometry" by calculating circle chord values to solve astronomical triangles and track planetary motion.
    • Ptolemy Writes the Almagest (c. 150 AD): Expands chord tables and spherical trigonometry principles, creating a comprehensive geometric framework that dominated astronomy for over a millennium.
    • Aryabhata Introduces the Sine Function (c. 499 AD): Indian mathematician defines jya (half-chord), shifting mathematical focus from full circle chords to the modern concept of sine.
    • Al-Battani and Islamic Golden Age Innovations (c. 900 AD): Islamic scholars formalize tangent, cotangent, secant, and cosecant functions, establishing trigonometry as an independent mathematical discipline.
    • Regiomontanus Publishes De Triangulis Omnimodis (1464): Produces the first European textbook devoted entirely to plane and spherical trigonometry, standardizing trigonometric methods for navigation.
    • Rheticus Defines Ratios on Right Triangles (1596): Defines trigonometric functions directly as ratios of triangle sides rather than circle chords, creating the modern textbook approach used today.
    • John Napier Invents Logarithms (1614): Revolutionizes trigonometric computation by simplifying complex multi-digit sine and cosine multiplications into straightforward addition and subtraction.
    • Leonhard Euler Unifies Trigonometry and Calculus (1748): Introduces standard function notations ($\sin, \cos, \tan$) and formulates Euler's formula ($e^{ix} = \cos x + i \sin x$), connecting trigonometry with complex analysis.

     

     

    Essential Trigonometry Formulas
    • Pythagorean Identity: $\sin^2\theta + \cos^2\theta = 1$
    • Tangent Identity: $\tan\theta = \frac{\sin\theta}{\cos\theta}$
    • Reciprocal Identities: $\csc\theta = \frac{1}{\sin\theta}$, $\sec\theta = \frac{1}{\cos\theta}$, $\cot\theta = \frac{1}{\tan\theta}$
    • Sine Angle Sum Formula: $\sin(A + B) = \sin A \cos B + \cos A \sin B$
    • Cosine Angle Sum Formula: $\cos(A + B) = \cos A \cos B - \sin A \sin B$
    • Sine Double-Angle Formula: $\sin(2\theta) = 2\sin\theta\cos\theta$
    • Cosine Double-Angle Formula: $\cos(2\theta) = \cos^2\theta - \sin^2\theta$
    • Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
    • Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos C$
    • Tangential Pythagorean Identity: $1 + \tan^2\theta = \sec^2\theta$

     

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