Trigonometry is a branch of mathematics dealing with relations involving lengths and angles of triangles. It can, in a simpler manner, be called the study of triangles. The angles are either measured in degrees or radians. We need to look into trigonometric formulae, ratios, functions etc. in order to grasp the concept completely.
Trigonometry is found all throughout
geometry, as every straight-sided shape may be broken into as a collection of
triangles. Further still, trigonometry has astoundingly intricate relationships
to other branches of mathematics, in particular complex numbers, infinite
series, logarithms and calculus. Online
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WHERE THE WORD TRIGONOMETRY CAME FROM?
The word trigonometry is a 16th-century
Latin derivative from the Greek words for triangle (trigōnon) and measure
(metron). Though the field emerged in Greece during the third century B.C.,
some of the most important contributions (such as the sine function) came from
India in the fifth century A.D. Because early trigonometric works of Ancient
Greece have been lost, it is not known whether Indian scholars developed
trigonometry independently or after Greek influence. According to Victor Katz
in “A History of Mathematics (3rd Edition)” (Pearson, 2008), trigonometry
developed primarily from the needs of Greek and Indian astronomers.
Types of triangles
A triangle is a well-defined bounded figure
consisting of three sides and three internal angles that add up to 180 degrees.
The types of triangles can be divided on the basis of length and angle. On the
basis of length, there are three types: scalene (all the sides and angles are
different), isosceles (2 sides and 2 angles are equal) and equilateral triangle
(all the sides and angles are equal). On the basis of angles, it is again
divided into three kinds: acute-angled triangle (all angles are less than 90
degrees), right-angled triangle (one angle is equal to 90 degrees), and
obtuse-angled triangle (one angle is greater than 90 degree).
BRANCH OF MATHEMATICS
Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.
Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using the trigonometric formulas, functions or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians. Some of the most commonly used trigonometric angles for calculations are 0°, 30°, 45°, 60° and 90°.
The trigonometric ratios of a triangle are
also called the trigonometric functions. Sine, cosine, and tangent are 3
important trigonometric functions and are abbreviated as sin, cos and tan. Let
us see how are these ratios or functions, evaluated in case of a right-angled
triangle.
Consider a right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.
The trigonometry angles
The trigonometry angles which are commonly
used in trigonometry problems are 0°,
30°, 45°, 60° and 90°. The trigonometric ratios such as sine, cosine and
tangent of these angles are easy to memorize. We will also show the table where
all the ratios and their respective angle’s values are mentioned. To find these
angles we have to draw a right-angled triangle, in which one of the acute
angles will be the corresponding trigonometry angle. These angles will be
defined with respect to the ratio associated with it.
