Trigonometric identities are the basic relation between the trigonometric ratio sinθ,cos , tanθ, cotθ, secθ, and cosecθ. Which are θ+ =1

1+ =** **

1+ =cosec2

These formulae are used to solve trigonometric functions and equation.

Sometimes used to calculate the value for trigonometric value of higher angle.

sin2A=2sinAcosA

cos2A=A -A

tan 2A =2tan A 1-A

These formulae are used to solve trigonometric functions and equation.

Sometimes used to calculate the value for trigonometric value of smaller angle.

sinA=2sin A2 cos A2

cosA=A2 -A2

Trigonometric function relates sides of triangle with the angle of that triangle, they often called as circular function also. The six trigonometry functions are sine, cosine, tangent, cotangent, secant, and cosecant.

This theorem relates three sides of the right angled triangle, which sates that square of the longest side of the triangle is equal to the sum of the square of the other two sides.

This a type of a triangle on the basis of angle and in this one we say, if one angle of triangle is 90° then that triangle is known as right angled triangle.

Equations in which we have trigonometric functions are known as trigonometric equation. In order to solve them we use trigonometric identities, formulae and some concept of inverse trigonometry.

Unit circle is circle with radius one and used in trigonometry to find the values and signs of higher angle. Using it we can also derive formulae of trigonometry.

All other types of triangles which are not right triangle can be called as no right triangles it includes all acute angled triangle and obtuse angled triangle.

**Question 1 - **A Tower is 100 ft high. At a certain distance a person is standing and notices that the angle of elevation with the ground to the top of the Tower is 60°. How far is the person from the base of the Tower?

**Solution 1 - **Given,

We have height of the Tower = 100 ft

The angle of elevation to top of the Tower = 60°

Let the distance of person form base of Tower is ‘d’

Now,

Tangent 60° = 100/d

√3 = 100d => d = 100/√3 => d = 1001.732 => d = 57.73672

**Question 2 - **From the top of a tall building of height 40 m, the angle of depression of the top of small tower is 50° whose height is 15 m. Find the distance between the two buildings.

**Solution 2 - **Given,

Height of the building = 40 m

Height of the tower = 15 m

Angle of depression = 50°

Let the distance between tower and the building is ‘d’

Now,

Tangent 50° = 30/d

1.1917 = 30/d => d = 30/1.1917=> d = 25.1741

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Trigonometry is derived from the Greek words -

** TRI** + **GON** + **METRON**

(three) (sides) (measures)

Trigonometry means measures of three sides and their relationship with angles. It is mostly used in right angled triangles.

There are many applications of trigonometry in real life. In all the situations, distances or heights can be found by using some mathematical techniques which come under the branch of mathematics called Trigonometry. Trigonometry is used to measure:

- the height of a building or mountains.
- used in construction.
- in navigation in the sea.
- used is physics and engineering.
- used in marine biology, criminology.
- solving complex equations & integrals of mathematics

**Trigonometric Ratios:**

**Sine = Opposite/Hypotenuse Cosecant = Hypotenuse/Opposite**

**Cosine = Adjacent/Hypotenuse Secant = Hypotenuse/Adjacent**

**Tangent = Opposite/A****djacent Cotangent = Adjacent/Opposite**

**Trigonometric ratios for an angle:**

Sine 60° = √3a/2a = √3/2 Secant 60° = 2/1

Cosecant 60° = 2/√3 Tangent 60° = √3a/a = √3/1

Cosine 60° = a/2a = 1/2 Cotangent 60° = 1/√3

**Trigonometric ratios for an angle:**

Sine 30° = a/2a = 1/2 Cosecant 30° = 2/1

Cosine 30° = √3a/2a = √3/2 Secant 30° = 2/√3

Tangent 30° = a/√3a = 1/√3 Cotangent 30° = 1/√3

**Trigonometric ratios for an angle:**

Sine 45° = a/√2a = 1/√2 Cosecant 45° = √2a/a = √2 1

Cosine 45° = a/√2a = 1/√2 Secant 45° = √2a/a = √2 1

Tangent 45° = aa = 11 Cotangent 45° = a/a = 1/1

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We use trigonometric ratio in order to find the missing side of the triangle if we have one side say adjacent then by using tangent ratio we can find the opposite side and by using cosine ratio we can find the hypotenuse.

Trigonometric ratio is the ratio of the sides of the right-angled triangle we named the three sides as the opposite, adjacent, and the hypotenuse, a ratio of these three sides with each other are known as a trigonometric ratio.

In order to learn trigonometry, first we should learn about the ratios how to find them if we have sides and If we have an angle, then the relationship between the two.

Learning Trigonometry is easy, all you need is the right approach. After all Trigonometry is all about the relationship between sides and angles of the triangles. Here’s what you need to do:

- Start from scratch by reviewing basic arithmetic, algebra and geometry
- Understand the role of Sine, cosine and tangent functions
- Learn the trigonometry table
- Solve textbook questions
- Focus on the solved examples

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Just like any other branch of Math, Trigonometry is hard only if you don't practice or have a weak foundation or need help in the basics of the subject.

So to conquer a subject like Trigonometry, you must know:

- Pythagoras theorem
- Be well versed with right angled triangle problems
- Know the basic functions and trigonometry table
- Invest time in solving old test papers
- Practicing equations daily

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According to the web, it was Hipparchus of Nicaea who is regarded as the “father of Trigonometry”. He even tabulated the values of the corresponding arc and chord for a series of angles. It is also said that the driving force behind inventing Trigonometry was Astronomy. Menelaus and Ptolemy are also known as important contributors in the field of Trigonometry.

Trigonometry is used for solving measurement problems. It is also used in:

- Marine Engineering
- To study Physics, Calculus
- Criminology
- Marine Biology
- Navigation
- Satellite systems
- Cartography
- Oceanography

Infact, if you want to measure a mountain or the height of the building, trigonometry applications will come into play. So take help in Trigonometry from qualified helpers to gain mastery in time.

Well as a student you are laying foundation to learn Trigonometry as you perform basic mathematical operations in arithmetic, algebra and geometry. As a subject it is introduced in higher grades.

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