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

    Trigonometric functions - Wikipedia
    The trigonometric functions most commonly used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less commonly used. Each of these six trigonometric functions has a corresponding inverse function and has an analog among the hyperbolic functions. The oldest definitions of ...

    Secant - Wikipedia
    Secant is a term in mathematics derived from the Latin secare ("to cut"). It may refer to: a secant line, in geometry the secant variety, in algebraic geometry secant (trigonometry) (Latin: secans), the multiplicative inverse (or reciprocal) trigonometric function of the cosine the secant method, a root-finding algorithm in numerical analysis, based on secant lines to graphs of functions a ...

    Secant function (sec) - Trigonometry - Math Open Reference
    Secant (sec) - Trigonometry function In a right triangle, the secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. In a formula, it is abbreviated to just 'sec'.

    secant - Wiktionary, the free dictionary
    secant (plural secants) (geometry) A straight line that intersects a curve at two or more points. (trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec

    Secant Calculator
    The secant calculator is here to help you find the value of the secant function of a given angle.

    Secant and Cosecant - Algebrica
    The secant and cosecant of an angle θ are defined as the reciprocals of cos(θ) and sin(θ), extending trigonometric relationships.

    SECANT Definition & Meaning - Merriam-Webster
    The meaning of SECANT is a straight line cutting a curve at two or more points.

    Secant Formula - Concept, Formulae, Solved Examples
    Secant is one of the six basic trigonometric ratios and its formula is secant (θ) = hypotenuse/base, it is also represented as, sec (θ). It is the inverse (reciprocal) ratio of the cosine function and is the ratio of the Hypotenus and Base sides in a right-angle triangle. In this article, we have covered, about Scant Formula, related examples and others in detail.

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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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