what is Trigonometry?

Answer 1

Trigonometry (from the Greek Trigona = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled triangles). Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, the trigonometric functions, and with calculations based on these functions.
The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.
The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.

Trigonometry has important applications in many branches of pure mathematics as well as of applied mathematics and, consequently, much of science. Trigonometry is usually taught in secondary schools, often in a precalculus course.

Overview

[edit] Basic definitions
In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.
In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.

The shape of a right triangle is completely determined, up to similarity, by the value of either of the other two angles. This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the size of the triangle. These ratios are traditionally described by the following trigonometric functions of the known angle:

* The sine function (sin), defined as the ratio of the leg opposite the angle to the hypotenuse.
* The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
* The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.

The adjacent leg is the side of the angle that is not the hypotenuse. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle.

\sin A=\frac{\textrm{opposite}}{\textrm{hypotenuse}} \cos A=\frac{\textrm{adjacent}}{\textrm{hypotenuse}} \tan A=\frac{\textrm{opposite}}{\textrm{adjacent}}=\frac{\sin A}{\cos A}

The reciprocals of these functions are named the cosecant (csc), secant (sec) and cotangent (cot), respectively. The inverse functions are called the arcsine, arccosine, and arctangent, respectively. There are arithmetic relations between these functions, which are known as trigonometric identities.

With these functions one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and an angle or two angles and a side or three sides are known. These laws are useful in all branches of geometry since every polygon may be described as a finite combination of triangles.

[edit] Extending the definitions
Graphs of the functions sin(x) and cos(x), where the angle x is measured in radians.
Graphs of the functions sin(x) and cos(x), where the angle x is measured in radians.

The above definitions apply to angles between 0 and 90 degrees (0 and π/2 radians) only. Using the unit circle, one may extend them to all positive and negative arguments (see trigonometric function). The trigonometric functions are periodic, with a period of 360 degrees or 2π radians. That means their values repeat at those intervals.

The trigonometric functions can be defined in other ways besides the geometrical definitions above, using tools from calculus and infinite series. With these definitions the trigonometric functions can be defined for complex numbers. The complex function cis is particularly useful

\operatorname{cis} (x) = \cos x + i\sin x \! = e^{ix}

See Euler's formula.

[edit] Mnemonics

The sine, cosine and tangent ratios in right triangles can be remembered by SOH CAH TOA (sine-opposite-hypotenuse cosine-adjacent-hypotenuse tangent-opposite-adjacent). It is referred to as "Sohcahtoa" by some mathematics teachers, who liken it to a fictitious Native American girl's or mountain's name.

Also, there are many different mnemonic sentences, usually nine words beginning with the letters "Sohcahtoa".

[edit] Calculating trigonometric functions

Main article: Generating trigonometric tables

Trigonometric functions were among the earliest uses for mathematical tables. Such tables were incorporated into mathematics textbooks and students were taught to look up values and how to interpolate between the values listed to get higher accuracy. Slide rules had special scales for trigonometric functions.

Today scientific calculators have buttons for calculating the main trigonometric functions (sin, cos, tan and sometimes cis) and their inverses. Most allow a choice of angle measurement methods, degrees, radians and, sometimes, Grad. Most computer programming languages provide function libraries that include the trigonometric functions. The floating point unit hardware incorporated into the microprocessor chips used in most personal computers have built in instructions for calculating trigonometric functions.

Answer 2

Trigonometry (from the Greek Trigona = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled triangles). Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, the trigonometric functions, and with calculations based on these functions.


The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.Trigonometry has important applications in many branches of pure mathematics as well as of applied mathematics and, consequently, much of science. Trigonometry is usually taught in secondary schools, often in a precalculus course.

Answer 3

Trigonometry (from the Greek Trigona = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled triangles). Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, the trigonometric functions, and with calculations based on these functions.
The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.
The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.

Trigonometry has important applications in many branches of pure mathematics as well as of applied mathematics and, consequently, much of science. Trigonometry is usually taught in secondary schools, often in a precalculus course.

Answer 4

Trigonometry (from the Greek Trigona = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled triangles). Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, the trigonometric functions, and with calculations based on these functions.


The Canadarm robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of the trigonometric functions of those angles.Trigonometry has important applications in many branches of pure mathematics as well as of applied mathematics and, consequently, much of science.


Basic definitions

In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.The shape of a right triangle is completely determined, up to similarity, by the value of either of the other two angles. This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the size of the triangle. These ratios are traditionally described by the following trigonometric functions of the known angle:

The sine function (sin), defined as the ratio of the leg opposite the angle to the hypotenuse.
The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
The adjacent leg is the side of the angle that is not the hypotenuse. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle.


The reciprocals of these functions are named the cosecant (csc), secant (sec) and cotangent (cot), respectively. The inverse functions are called the arcsine, arccosine, and arctangent, respectively. There are arithmetic relations between these functions, which are known as trigonometric identities.

With these functions one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and an angle or two angles and a side or three sides are known. These laws are useful in all branches of geometry since every polygon may be described as a finite combination of triangles

Answer 5

This is a very important field of geometry in particular and overall of mathematics.
It is the knowledge of triangles.
In history Egyptians at the time of Pharaohs were the expert of Trigonometry, as they were able to redefine their land property lines, in the shape of triangles, when the marks were used to be omitted by yearly routine of flooding water in the river Nile, over their agricultural lands.
For any kind of engineering field, the knowledge of Trigonometry is must to be known.

Answer 6

Trigonometry is math that deals specifically with triangles...

And people... Read other peoples' answers, before using the same exact info twice!!!

Answer 7

the process of measuring three angles of a triangle is known as trigonometry....

Answer 8

The study of motion within the limits of geometry. Look up Wikipedia.com

Answer 9

trigonometry is to do with sin,cos and tan and angles.

Answer 10

you will get all the information related to Trignometry at this below link:

http://www.sosmath.com/trig/trig.html