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Related Concept Videos

Inverse Trigonometric Functions01:29

Inverse Trigonometric Functions

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Inverse trigonometric functions are fundamental mathematical tools that reverse the actions of standard trigonometric functions. While trigonometric functions map angles to ratios, inverse trigonometric functions perform the opposite operation by mapping a ratio back to its corresponding angle. These functions are essential in various applications, particularly in determining angles when given specific distances, such as calculating elevation angles in navigation and engineering.For a function...
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Inverse Hyperbolic Functions and Their Derivatives01:25

Inverse Hyperbolic Functions and Their Derivatives

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The shape of a suspension bridge cable hanging under its own weight is described by a catenary curve, which is modeled using the hyperbolic cosine function. This mathematical model accurately captures the balance between gravity and tension acting along the cable. When a particular vertical position on the cable is known, the corresponding horizontal position can be determined using the inverse hyperbolic cosine function, allowing for a detailed analysis of the cable's geometry.Inverse...
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Derivatives of Inverse Trigonometric Functions01:30

Derivatives of Inverse Trigonometric Functions

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A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle...
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Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

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An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
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Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
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Emission Spectra02:39

Emission Spectra

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When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a range of energies, and thereby produce a continuous spectrum in which an unbroken series of wavelengths is present.
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Related Experiment Video

Updated: Feb 13, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Inverse problem of quartic photonics.

Thomas Mulkey, Jimmy Dillies, Maxim Durach

    Optics Letters
    |March 16, 2018
    PubMed
    Summary

    We developed a method to design metamaterials by engineering their quartic k-surfaces. This approach allows precise control over plane wave propagation for advanced photonic applications.

    Area of Science:

    • Physics
    • Materials Science
    • Optics

    Background:

    • Metamaterials offer unique electromagnetic properties.
    • Designing metamaterials with specific wave propagation characteristics is challenging.
    • Quartic k-surfaces represent a complex but potentially powerful class of metamaterial designs.

    Purpose of the Study:

    • To formulate and solve the inverse problem for quartic photonics.
    • To enable the engineering of metamaterial effective parameters from desired plane waves.
    • To explore applications in high-k limits, non-reciprocity, and bi-anisotropic media.

    Main Methods:

    • Formulation of the inverse problem for quartic k-surfaces.
    • Solving the inverse problem to determine material parameters.

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  • Application of the method to specific design targets.

    • Main Results:

    • A novel approach to design metamaterials with quartic k-surfaces.
    • Demonstrated ability to engineer effective parameters for desired plane waves.
    • Successful application to designing for high-k limits, extreme non-reciprocity, and complex bi-anisotropic media.

    Conclusions:

    • The developed inverse problem method provides a powerful tool for designing advanced metamaterials.
    • This work opens new avenues for creating novel photonic devices with tailored wave propagation.
    • The approach is versatile and applicable to a range of challenging metamaterial designs.