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# Trigonometry Techniques

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7 Reviews

I teach all techniques in Trigonometry actually it is a one tough subject I can deal it easy way and I assume that you love my teaching. Like how to take sin angle and cos angle. Every student will face difficult in exam while dealing this subject and don't know how to take angle in trigonometry. And you will learn easy table to remember all angles. Like

## Sine, Cosine and Tangent

The main functions in trigonometry are Sine, Cosine and Tangent

They are simply one side of a right-angled triangle divided by another.

For any angle "Î¸":

(Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)

### Example: What is the sine of 35Â°?

Using this triangle (lengths are only to one decimal place):

sin(35Â°) = Opposite Hypotenuse = 2.84.90.57...

Trigonometry is defined as one of the branches of mathematics that deals with the relationships that involve lengths and also the angles of triangles. In a simple manner, we can say that Trigonometry is the study of triangles. The word trigonometry was derived from the Greek word, where, â??TRIâ?? means Threeâ??GONâ?? means sides and whereas the â??METRONâ?? ways to measure. This concept is given to us by a Greek mathematician Hipparchus.

To be more specific, trigonometry is all about a right-angled triangle, where one of the internal angles measure about 90Â°. Moreover, it is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle. In trigonometry, the angles are either measured in radians or degrees.

This branch divides into two sub-branches called plane trigonometry and the spherical geometry. Trigonometry, in general, is about the trigonometric formulas,  trigonometric ratios, and functions, Right-Angled Triangles, etc. Let us study all these topics in detail.

### Trigonometric Functions and Ratios:

The trigonometric ratios of a triangle are also called the trigonometric functions. There are three essential trigonometric functions in trigonometry known as Sine, cosine, and tangent and abbreviated as Sin, Cos, and Tan. How are these ratios or functions, evaluated in the case of a right-angled triangle?

Consider the right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse is referred to as the adjacent and opposite. The trigonometric functions or the ratios of this triangle is calculated by the below formulas.

• Sine ratio or Function is given as, sin Î¸ = Opposite / Hypotenuse

• Tangent ratio or Function is given as, tanÎ¸ = Opposite / Adjacent

• Cosine ratio or Function is given as, cos Î¸ = Adjacent / Hypotenuse

Similar to the ratios sine, cosine and tangent, there are other three trigonometric ratios or functions in trigonometry called Cotangent,  Cosecant, and Secant. The values of these trigonometric functions are evaluated by using the following formulas

• Cosecant Function- cosec Î¸ = Hypotenuse / Opposite

• Cotangent Function- cot Î¸ = Adjacent / Opposite

• Secant Function â?? sec Î¸ = Hypotenuse / Adjacent

### Inverse Trigonometric Ratios:

The inverse trigonometric functions are those functions which involve the inverses of cosine, tangent, and Sine. These opposites, are called as inverse trigonometric functions. By considering the right-angled triangle, the inverse functions, are given below-

• Cosec Î¸ = 1/sin Î¸ = Hypotenuse/opposite

• Cot Î¸ = 1/Tan Î¸ = adjacent / opposite

• Sec Î¸ = 1/Cos Î¸ = hypotenuse/ adjacent

### Trigonometric Ratios of Specific Angles:

Suppose if you are given the question â?? In a right-angled triangle ABC, if one side of the triangle is 45Â°, then what is the value of other side or angle?

For such questions, the below table will help you out in finding the trigonometric and inverse trigonometric ratios of different Angles of a triangle.

### Pythagoras Theorem:The Pythagoras Theorem helps to know the relationship between the trigonometric identities, which, is discussed in the next sub-heading.

Pythagoras theorem states â?? the square of the hypotenuse (c )equals to the sum of the squares of the adjacent( b ) and opposite ( a).â??

In equation form, it is, given as: c2  =a2 + b2

Trigonometric Identities:

An identity is a form of equation true for all the values of the variables, which both the sides of an equation is defined. These variables are either in the shape of a statement or even specified. The Pythagoras theorem is also one of the Trigonometric Identities. The Trigonometric Identities are the equations which are true in the case of Right Angled Triangles.

Some of the other identities or rather say formulas in trigonometry, are as given below-

1. #### Pythagorean Identities-

• Sin Â² Î¸ + cos Â² Î¸ = 1

• tan 2 Î¸ + 1 = sec2 Î¸

• Cot2 Î¸ + 1 = cosec2 Î¸

• sin 2Î¸ = 2 sin Î¸ cos Î¸

• cos 2Î¸ = cosÂ² Î¸ â?? sinÂ² Î¸

• tan 2Î¸ = 2 tan Î¸ / (1 â?? tanÂ² Î¸)

• cot 2Î¸ = (cotÂ² Î¸ â?? 1) / 2 cot Î¸

1. #### Sum and Difference identities-

sin(Ï?/2â??u)=cosucos(Ï?/2â??u)=sinutan(Ï?/2â??u)=cotu

cosec(Î /2â??u)=sec(u)sec(Î /2â??u)=cosec(u)cot(Î /2â??u)=tan(u)

• #### Sine Laws-

a/sin(A)=b/sin(B)=c/sin(C)=2R=abc/2Î?

Area=Î?=1/2absin(C)

• #### Cosine Laws-

Area=Î?=â??s(sâ??a)(sâ??b)(sâ??c)=abc/4R

• #### Tangent Laws-

(aâ??b)/(a+b)=tan[1

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