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Over the decades now, trigonometry has lived the moment, advancing and excelling in our education system. Too many scholars trig, as they call it, sounds like any other regular, and complex topic in math.

However, the main question is, what is trigonometry? In this article, we delve deep and take a look at what it means and entails. You can seek for a trigonometry homework solver now by simply getting in touch with us for prompt help.

Definition and History

Trigonometry is simply a branch of math that studies triangles. To be more specific, it tends to explain the study of relationships between angles and sides of a triangle. The subject matter plays a central role as a branch of mathematics, relating to other scientific and mathematics disciplines. Some of these fields include calculus, geometry, complex numbers, and logarithms, to mention a few.

With enthusiastic research over the centuries, the subject progressed with more functions and content hence making trigonometry not just about triangles. Due to this, trig is useful in studying hyperbola measuring, ellipse measuring, circle measuring to mention a few. It is also applied in variable manipulation and uses functional ratios between sides and angles of triangles.

The term trigonometry takes us back to the 16th century. Greek-derived it in Latin words, 'trigonon' meaning triangle and 'metron' indicating measure. A combination of the two terms gives a triangle measure, which is similar to the theme's definition. However, the subject matter originated many centuries back.

It was first used in the ancient Middle East in the third century B.C. It later moved to Greece, India, medieval Arabia, and Europe. Existence of trade and immigration of merchants across the borders was the main contributor to the spread of the subject's knowledge. Europe is the last point enhanced the modification of the theme to the current version that is modern trigonometry, commonly used in our education system.

As the knowledge spread across the borders, every state tried to improve the subject coming up with several contributions. Arabia and India progressed their study and research making it a little bit complicated for others to articulate the contents.

Remarkable contributions were noted though. For instance, an Indian mathematician, Madhava, discovered the sine function that was highlighted in his work, '1400 discovery of an infinite series of sine.' These contributions were however unknown in Europe until 1670, when Sir Isaac Newton made his independent discovery.

With all these different discoveries, it brought about confusion and complications with the timeline of trigonometric development. In the 17th century B.C., a Neo Babylonia scholar, Hypsicles of Alexandria discovered a trigonometric technique that could be used in computing the rise times of fixed stars on the zodiac.

It has primarily led to the existence of the calendar system highlighting the 365 days forming a year. Uta Merzbach asserted in his book, 'A History of Mathematics' that the adaptation of Hypsicles technique was an inspiration to Hipparchus hence beginning the trend of cutting the circle into 360 degrees.

Hipparchus of Nicaea applied the knowledge of geometry in determining the values of trigonometry for increments of 7.5 degrees. Later on, Ptolemy of Alexandria modified Hipparchus work by ascertaining the values for increases of 0.5 degrees that is 0 to 180 degrees.

Trigonometric Functions

These are the functions that are utilized in relating the angles of a triangle to the ratios of the length of two sides. These functions are widely used in all scientific and engineering fields that are related to geometry.

In the 17th and 18th centuries, the subject matter began spreading all over Europe, leading to its development to modern trigonometry. This development was trail blazed by great minds such as Sir Isaac Newton and Leonard Euler. They are considered to still being the best mathematicians to date. Euler's formula established the fundamental relations between the trigonometric functions.

Trigonometric functions assist in interpreting and relating the length of sides with angles. The three main ratios used are the sine abbreviated as sin(x), the cosine abbreviated as cos(x) and lastly tangent abbreviated as tan (x).

These functions also have reciprocal ratios, though they aren't commonly used. These include the secant abbreviated as arcsin(x), cosecant abbreviated as arccos(x) and contangent abbreviated as arctan(x). To comprehend these functions well, you need to understand the parts and terminologies of a triangle.

An adjacent is known as the side and angles that are merged, whereas the opposite is the side and angles that are not fused. On the other hand, the hypotenuse is the side that is opposite to the right angle triangle. The hypotenuse derives it term from Latin meaning stretching under. The other two sides opposite the hypotenuse of a right-angle triangle are known as legs.

Enacting these functions to an angle measure produces the various combinations of ratios of the lengths of the triangle sides. The cosine of an angle is the division of the length of the adjacent side by the length of the hypotenuse. The angle of the sine function is the division of the length of the opposite side by the length of the hypotenuse. Remember that the trigonometric functions relate to each other via a great variety of complex equations called identities.

Significance of the Study of Trigonometry

The subject is not only limited to right-angled triangles. It can also be used with all shapes and triangles that have straight lines and can be treated as a triangle. The field involves functions that play a crucial role in educating a student on the calculation of angles, and dimensions of various shapes.

This aspect is also crucial for designers and engineers while preparing plans for their projects. Trigonometry is also significant in offering a broad scope of career options. The theme subject works for hand in hand with several sciences and mathematical fields hence equipping one with the necessary skills.

Trigonometry skills are also useful to students as it aids them in calculating the distance between two points of any triangle. It is also helpful in providing accuracy while working out the angles and sides of triangles.

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