trigonometry

(noun)

The branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, particularly the trigonometric functions.

Examples of trigonometry in the following topics:

  • Trigonometry and Complex Numbers: De Moivre's Theorem

  • Trigonometry

    • Trigonometry is central to the use of free body diagrams, which help visually represent difficult physics problems.
    • Trigonometry is also used in determining the horizontal and vertical components of forces and objects.
    • When the force or object is not acting parallel to the x or y axis, people can employ basic trigonometry to use the simplest components of the action to analyze it.
    • Given the finished free body diagram, people can use their knowledge of trigonometry and the laws of sine and cosine to mathematically and numerical represent the horizontal and vertical components:
    • Explain why trigonometry is useful in determining horizontal and vertical components of forces

  • Converting Between Polar and Cartesian Coordinates

    • Polar and Cartesian coordinates can be interconverted using the Pythagorean Theorem and trigonometry.

  • Polar Coordinates

    • Thus, using trigonometry, it can be shown that the $x$ coordinate is $r \cos \theta$ and the $y$ coordinate is $r \sin \theta$.

  • Triple Integrals in Spherical Coordinates

    • Finally, you obtain the final integration formula: It's better to use this method in case of spherical domains and in case of functions that can be easily simplified, by the first fundamental relation of trigonometry, extended in $R^3$; in other cases it can be better to use cylindrical coordinates.

  • Trigonometric Functions

  • The Ray Aspect of Light

    • The movement of light, as a ray, can be shown with simple geometry and trigonometry.

  • Right Triangles and the Pythagorean Theorem

    • The relation between the sides and angles of a right triangle is the basis for trigonometry.

  • The Law of Sines

    • Previous concepts explained how to use trigonometry to find the measures of the angles and sides of right triangles.

  • Brief Overview of Cranial Nerves

    • One that may be helpful is: Old Opie Occasionally Tries Trigonometry And Feels Very Gloomy, Vague And Hypoactive.