We have already learnt that trigonometry is the study of relationships between the sides and angles of a triangle. The ratios of the sides in a right triangle with respect to its acute angles are called trigonometric ratios of the angle. The angles and are useful angles in trigonometry, and their numerical values are easy to remember. When two angles add up to 900, then any one angle is the complement of the other. Trigonometric ratios of complementary angles help in simplifying problems.

sin000, tan00, cot00, sec00, cosec00, trigonometric ratios of special angles, values of trigonometric ratios at 00 sin000, tan00, cot00, sec00, cosec00, trigonometric ratios of special angles, values of trigonometric ratios at 00

sin900, cos900, tan900, cot900, sec900, cosec900, trigonometric ratios of special angles, values of trigonometric ratios at 9006

sin450, cos450, tan450, cot450, sec450, cosec450, trigonometric ratios of special angles, values of trigonometric ratios at 450sin450, cos450, tan450, cot450, sec450, cosec450, trigonometric ratios of special angles, values of trigonometric ratios at 450

sin600, cos600, tan600, cot600, sec600, cosec600, trigonometric ratios of special angles, values of trigonometric ratios at 600sin600, cos600, tan600, cot600, sec600, cosec600, trigonometric ratios of special angles, values of trigonometric ratios at 600

sin300, cos300, tan300, cot300, sec300, cosec300, trigonometric ratios of special angles, values of trigonometric ratios at 300sin300, cos300, tan300, cot300, sec300, cosec300, trigonometric ratios of special angles, values of trigonometric ratios at 300

...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These well-defined geometric relationships can be useful when teaching...

...Right Triangle TrigonometryTrigonometry is a branch of mathematics involving the study of triangles, and has applications in fields such as engineering, surveying, navigation, optics, and electronics. Also the ability to use and manipulate trigonometric functions is necessary in other branches of mathematics, including calculus, vectors and complex numbers. Right-angled Triangles In a right-angled triangle the three sides are given special names....

...Trigonometry
| Introduction to trigonometryAs you see, the word itself refers to three angles - a reference to triangles. Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used: 1. In geometryIn its geometry application, it is mainly used to solve...

...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for...

...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical...

...non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
There is an enormous number of applications of...

...Early trigonometry
The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the...

...The Way Trigonometry is used in Astronomy
By: Joanna Matthews
Practical Applications of Advanced Mathematics
Mrs. Amy Goodrum
July 15, 2003
Abstract
This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas, such as engineering, chemistry, surveying, and physics, it is mainly used in astronomy Trigonometry is used to find the distance of stars, the distance from one planet to...

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