## Trigonometry

Subject: Optional Mathematics

### Lesson Info

• Notes 6
• Videos 19
• Exercises 66
• Practice Test 82
• Skill Level Medium

#### Measurement of Angle

The following three systems are commonly used in the measurement of angles: a) Sexagesimal system (degree system): This system is also called British System. In this system, the unit of measurement is degree. So, this system is also known as degree system. b) Centesimal system (grade system): This system of measurement is also called the French system. In this system, the unit measurement is grade.So this system is also known as grade system

#### Trigonometrical Ratio

Let us consider a right-angled triangle ABC in which ∠ABC = 90°. This triangle consists of a right angle, two acute angles and three sides. These are called elements of a right-angled triangle. One of the acute angles is considered as the reference angle. This reference angle is used for naming the sides of a right-angled triangle. The side opposite to the reference angle is called perpendicular and it is denoted by the letter p. This side opposite to the right angle is called hypotenuse and it is denoted b

#### Trigonometric Function

Different standard angles are taken as a variable in the trigonometric function. For different angles, the values of trigonometric ratios will also be different. Take the angles of x-axis and values of trigonometric ratios in y-axis Join the points freely to obtain the graph of the trigonometrical ratio.

#### Trigonometric Ratios of Some Standard Angles

Different angles have a different value with various trigonometric ratios. We shall consider 0°, 30°, 45° and 90° as the standard angles and we shall learn their values here. In this unit, we shall verify the values of 0°, 30°, 45° and 90° using geometrical proofs. Different angles have a different value with various trigonometric ratios. We shall consider 0°, 30°, 45° and 90° as the standard angles and we shall learn their values here. In this unit, we shall verify the values of 0°, 30°, 45° and 90° using geometrical proofs.

#### Trigonometric ratios of any angle

This note includes all the information of Trigonometrical ratios of angle generalized and associated with a given angle theta.

Any allied angle can be in the form (n × 90° ± $\theta$) where n is an integer. We can change the trigonometric ratios of the angle (n × 90° ± $\theta$) into the trigonometric ratio of an angle $\theta$.