Introduction to trigonometry class 10 notes provided here gives an in-depth understanding of this chapter in a concise way. Students can refer this notes to learn the concepts in a better way and use it during revision time to quickly browse this topic easily. This class 10 chapter 8 notes cover the following-

- What is trigonometry
- Trigonometric ratios
- Trigonometric ratio table
- Some important formulas
- Example Questions
- Practice Questions

## What is Trigonometry?

Trigonometry is the study of relationships between the angles and sides of a triangle. This word is derived from three the Greek words which. ‘tri’ (three), ‘gon’ (sides) and ‘metron’ (measure).

In simple words, trigonometry is the study of relationships between the sides and angles of a triangle. Trigonometry was used to find out the distances of the stars and planets from the Earth in the earlier days.

In a right triangle, the ratio of sides can be represented as a trigonometric angle. We will calculate the ratio of some standard angles and establish identities involving these ratios, known as trigonometric identities.

### Trigonometric Ratios

There are three main trigonometric ratios which are:

- Sine ratio = Opposite / Hypotenuse
- Tangent ratio = Opposite / Adjacent
- Cosine ratio θ = Adjacent / Hypotenuse

There are three more ratios which are opposite to the aforementioned ratios. These ratios are-

- Cosecant Function = 1/ Sin = Hypotenuse / Opposite
- Cotangent Function = 1/tan = Adjacent / Opposite
- Secant Function = 1/Cosine = Hypotenuse / Adjacent

In a right triangle ABC, right-angled at B, Side AB is called as base(B), BC is called as Perpendicular(P) and side AC is called as Hypotenuse(H).

From the above diagrams, the trigonometric ratios of angle A in a right triangle ABC are defined as follows-

\(Sin\, A = \frac{P}{H} = \frac{BC}{AC}\)\(Cos\, A = \frac{B}{H} = \frac{AB}{AC}\)\(Tan\, A = \frac{P}{B} = \frac{BC}{AB}\)\(Cot\, A = \frac{B}{P} = \frac{AB}{BC}\)\(Sec\, A = \frac{H}{B} = \frac{AC}{AB}\)\(Cosec\, A = \frac{H}{P} = \frac{AC}{BC}\)### Trigonometric Ratio Table

Angle |
0° | 30° | 45° | 60° | 90° |

Sin A | 0 | 1/2 | 1/√2 | √3/2 | 1 |

Cos A | 1 | √3/2 | 1/√2 | 1/2 | 0 |

Tan A | 0 | 1/√3 | 1 | √3 | Not Defined |

Cosec A | Not Defined | 2 | √2 | 2/√3 | 1 |

Sec A | 1 | 2/√3 | √2 | 2 | Not Defined |

Cot A | Not Defined | d√3 | 1 | 1/√3 | 0 |

### Some Important Trigonometric Formulas

- sin (90 – A) = cos A, cos (90 – A) = sin A
- tan (90 – A) = cot A, cot (90 – A) = tan A
- sec (90 – A) = cosec A, cosec (90 – A) = sec A.
- sin2 A + cos2 A = 1
- sec2 A – tan2 A = 1 for 0° ≤ A < 90

cosec2 A = 1 + cot2 A for 0° < A ≤ 90

Check out all the important trigonometry formulas in this article and be able to solve any question easily. These formulas are extremely important and can help students to have a complete understanding of this topic.

### Example Question

### Practice Questions

- Find the value of (sec A + tan A) (1 – sin A)
- Prove \(\frac{Cos\, A}{1+sin\,A}+\frac{1+sin\,A}{cos\,A}=2\,sec\,A\)
- \(\frac{1}{tan\,A+cot\,A} = \left ( cosec\,A-sin\,A \right )\left ( sec\,A-cos\,A \right ).\) Prove this.

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