Many applications in our daily life involve trigonometry. Some of these applicat

Question

Many applications in our daily life involve trigonometry. Some of these applications are things with a predictable pattern, such as temperatures, ocean tides, and time. A function that represents values in a regular pattern is called a periodic function. Sine and Cosine functions are periodic functions.

Research where periodic functions are used and choose and explain one specific application.

Here's an example. The sine wave is important in electronics, as the intensity of an alternating current can be modeled by a sine wave. The current of a direct current full-wave rectification system, used to convert AC into DC, can be modeled using an absolute value sine wave. Also, electric current is transmitted around the country in the form of alternating current: 120 volts and 60 Hz (polarity changes between positive to negative back to positive). Alternating current is what powers your coffeemaker when you brew your coffee in the morning!

Explanation / Answer

There is an enormous number of applications of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields which make use of trigonometry or trigonometric functions include astronomy (especially, for locating the apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

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