Question

what is trigonometry?​

Answer 1

Trignometry :-

Trignometry is a branch of mathematics which helps to measure the angles of a Triangle

In Trignometry we use only Right angles triangle

Trignometry is a greek word which means Trigon + metron

Three angles measurement

Angle :-

Angle can be represented theta , alpha etc

The amount of rotation of ray is called angle

Angle can be measured in different methods

Our Indian system (Radian)

Pythagoras theoram :-

In a right angle triangle ,

Square of hypotenuse = sum of squares of remaining two sides

AC² = AB² + BC²

What is Trignometric ratios Introduction?

There are 6 Trignometric ratios

They are

sinθ

cosθ

tanθ

cscθ

secθ

cotθ

Here θ is measure of angle Without angle there is meaningless for word sin , cos , tan etc

All these Trignometric ratios are Depends on angle

cosec θ is reciprocal of sinθ

secθ is reciprocal of cosθ

cotθ is reciprocal of tanθ

First we will know Formulaes for Trignometric ratios

Once observe diagram in attachment

The opposite to θ is called opposite side

The adjacent side to θ is called adjacent side

The side which is opposite to 90° is called hypotenuse

Now ,

sinθ = $\sf\dfrac{opposite\: side}{hypotenuse}$

cosθ = $\sf\dfrac{adjacent\:side}{hypotenuse}$

tanθ = $\sf\dfrac{opposite \:side}{adjacent \: side}$

cosecθ = $\sf\dfrac{hypotenuse}{opposite\:side}$

secθ = $\sf\dfrac{hypotenuse}{adjacent\:side}$

cotθ = $\sf\dfrac{adjacent\:side}{opposite \:side}$

By observing these

We can say that

cosecθ = 1/sinθ

secθ = 1/cosθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

These are called Trignometric relations

Now , Trignometric table

Refer attachemnt

In place of θ we Substitute angles like 30°,46°,90°,60°,0°

We get values

_______________________

Trignometric Identities

These also very important

There are 3 Identities

sin²θ+ cos²θ = 1

sin²θ = 1- cos²θ

cos²θ = 1-sin²θ

__________________

sec²θ - tan²θ = 1

From a² - b² = (a + b)(a-b)

(secθ+ tanθ) (secθ-tanθ) = 1

secθ + tanθ= 1/secθ-tanθ

secθ - tanθ = 1/secθ+ tanθ

____________________

cosec² -cot²θ = 1

Similarily

(cosecθ + cotθ) ( cosecθ - cotθ) = 1

cosecθ + cotθ = 1/cosecθ - cotθ

cosecθ - cotθ = 1 /cosecθ + cotθ

_____________________

These are the main basics of Trignometry If you learn these properly U can solve Trignometric problems easily

Answer 2

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• Trigonometry is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees. The commonly used trigonometry angles are 0°, 30°, 45°, 60° and 90°.

• Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus.