**CONTENT LIST**

## **Trigonometry**

The branch of mathematics that deals the properties of trigonometric functions and their application to the determination of the angles and sides of triangles.

### **Angle**

When a ray AB starting from its initial position and rotates about its end point A and takes the final position AC, we say that an angle BAC (written as ∠ BAC) has been formed.

The amount of rotation from the initial side AB to the terminal side AC is termed as the measure of the angle.

### **Positive and Negative Angles**

**Positive Angles**

An angle formed by a rotating ray is said to be positive if rotation is anticlock wise.

**Negative Angles**

An angle formed by a rotating ray is said to be negative if rotation is clock wise.

### **Measurement of Angles**

There are three system for measuring angles,

- Sexagesimal System(Degree Measure)
- Centesimal System
- Circular System (Radian System)

**Sexagesimal System(Degree Measure)**

In Sexagesimal System, a right angle is divided into 90 equal parts,one part is known as degree. Symbol ° is used to expres degree.

One degree is divided into 60 equal parts, termed as minutes.Symbol ′ is used to expres minutes.

One minute is divided into 60 equal parts, termed as seconds. Symbols ″ are used to denote seconds.

**Centesimal System **

In Centesimal System, a right angle is divided into 90 equal parts, one part is known as grades.

One grades is divided into 100 equal parts, termed as minutes.Symbol ′ is used to expres minutes.

One minute is divided into 100 equal parts, termed as seconds. Symbols ″ are used to denote seconds.

**Circular System (Radian System)**

In this system, angle is measured in term of radian.

A radian is the angle subtended at the centre of a circle by an arc of equal length of radius of the circle.

**Relation between radian and degree
π radian = 180°**

## **Trigonometric Ratios**

Trigonometric ratios or T-ratios express relation between different sides and angles of a right angled triangle.

There are six trigonometric ratios or T-ratios.These are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

sine: Sine of an angle is the ratio of perpendicular to the hypotenuse.

cosine: Cosine of an angle the ratio of the base to the hypotenuse.

tangent: Tangent of an angle is the ratio of perpendicular to the

cosecant: Cosecant is a multiplicative inverse of sine.

secant: Secant is a multiplicative inverse of cosine.

cotangent: Cotangent is the multiplicative inverse of the tangent.

## **Quadrent**

The x-axis and y-axis of a two-dimensional Cartesian plane system divide the plane into four regions called quadrants.

## **How to find value of trigometric function of any angle?**

Step 1: Convert the given angle in term of (Nx90°+θ°)

Step 2:
Case A: If N= even number than there will no change in trigonmetric function .

Case B: If N= odd number than there will change in trigonmetric function .

- sin will change to cos .
- cos will change to sin .
- tan will change to cot .
- sec will change to cosec .
- cosec will change to sec .
- cot will change to tan .

Step 3: Idenify the quadrent of given angle and give sign +/- accordingly .

**Example:1**

**Example:2**

Test your understanding

a) (√3 – 1) / √2

b)(√3 – 1) / 2√2

c)(√3 – 1) / 2

d) None of these

** Solution**

sin15° = (1/√2 . √3/2) – (1/√2 . ½)

sin15° = (√3 – 1) / 2√2

a) 1

b) cos56°

c) sin28°

d) None of these

** Solution**

cos(2A) = cos²A - sin²A

putting A=28°

cos²(28°)−sin²(28°)= cos56°

a) sin(10x)

b) 3sin²(10x)

c) 3sin(10x)

d) None of these

** Solution**

sin(2A) =2sinA.cosA

putting A=5x

6sin(5x)cos(5x)= 3sin(10x)

a) sin(34°)

b) cos²(34°)

c) cos(34°)

d) None of these

** Solution**

cos(2A) = 1 - 2sin²A

putting A=17°

1−2sin²(17°)=cos(34°)

Related Topics