By Truemaths Tech, Last Updated 22 Jul, 2023 3 min read

**Trigonometry formulas for class 10**

**Trigonometry** is the most important chapter for students whether they are studying in **CBSE/****ICSE** boards or preparing for competitions like IIT or SSC. In CBSE/ NCERT Trigonometry chapter is introduced in **class 10th** (Chapter 8), and in ICSE it is introduced in class 9th. Most of the time students find the chapter Trigonometry very difficult to understand and very hard to learn all the **Trigonometry formulas**. In this article, You’ll find all ** trigonometric formulas for class 10**.

After reading this article what will you understand:-

- In this article, we will try to help students to make them understand trigonometry easily.
- We will make some
so that the Trigonometry formulas for class 10 become easy to learn.**short tricks** - Also, you don’t have to Rote-learn all of them. Instead, you will develop a technique so that some of the formulas can be
**derived**, instead of memorizing them.

This word Trigonometry basically came from combining two Greek words “trigōnon” which means “triangle” and “metron” which means “measure”.Thus, it is used to *measure Triangles.*

In simple words, **Trigonometry is a branch of Mathematics where we study relationships between side lengths and angles of triangles.** **Trigonometry formulas for class 10**

Now, let me make this simpler!

- QUESTION (i):- if we are given two sides of a right-angled triangle and we are asked to find the third side, What mathematical concept will we use to find the third side?

ANSWER:- Obviously, this is very simple! We will use**Pythagoras’ theorem**. - QUESTION (ii):- If we are given one side and one angle (other than 90°) of a
**right-angle triangle**and you were asked to find the remaining sides of this triangle, how will you find it?

ANSWER:- For this, you will have to understand a new concept known as “Trigonometry”.

Most of the time we wonder **what is the use of Trigonometry** in our life?. You may not have applied Trigonometry directly in solving your day to day life problems, but indirectly it is used in various things that we see around us.

- How do you think we came to know that height of the
**Mount Everest**is 8848 meters. Obviously, by using trigonometry. - How we came to know that the distance between “Earth” and “Sun”? when we have never been to “Sun”. you can measure the distance of nearby objects in space by using Trigonometry a method called
**Trigonometric parallax**or**Stellar parallax.** - The
**sine and cosine functions**(which you will study later) are fundamental to the theory of periodic functions, those that describe the sound and light waves. - Trigonometry is also used in construction, Video games, flight engineering, marine engineering, archaeology, criminology, navigation, oceanography, cartography (creation of maps), satellite systems.
- Well to your surprise almost every scientific discovery that is related to distance is proved only because of Trigonometry.

NOTE:- We have discussed these **Real-life applications of Trigonometry** thoroughly in this article, please go through it.

First of all, we will discuss what are **Trigonometric ratios**. Trigonometric Ratios are basically a relationship between the measurement of the angles and the lengths of the sides of the right triangle.

Now let’s discuss how many types of Trigonometric ratios can be possible.

In a right-angled triangle, we have three sides named (H) Hypotenuse (longest side), (P) Perpendicular(opposite side to the angle), and (B) **Base**. If we are asked to take any two sides out of these three sides and form a ratio we will find that six ratios are possible (P/H, B/H, P/B, H/P, H/B, B/P). We have assigned a particular name to each of the ratios.

- sinθ = (Perpendicular(P))/( Hypotenuse(H)).
- cosθ = (Base(B))/( Hypotenuse(H)).
- tanθ = (Perpendicular(P))/(Base(B)).
- cosecθ = (Hypotenuse(H))/(Perpendicular(P)).
- secθ = (Hypotenuse(H))/(Base(B)).
- cotθ = (Base(B))/(Perpendicular(P)).

- sin θ = 1/(cosec θ)
- cosec θ = 1/(sin θ)
- cos θ = 1/(sec θ)
- sec θ = 1/(cos θ)
- tan θ = 1/(cot θ)
- cot θ = 1/(tan θ)

tanθ = (sin θ ) / (cos θ )

cot θ = (cos θ ) / (sin θ )

This **Trigonometric ratios table** helps us to find the values of **trigonometric standard angles** such as 0°, 30°, 45°, 60°, and 90°.

Trigonometric Ratios | 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 |

cot A | Not defined | √3 | 1 | 1/√3 | 0 |

cosec A | Not defined | 2 | √2 | (2√3)/3 | 1 |

sec A | 1 | (2√3)/3 | √2 | 2 | Not defined |

Now there are certain **Trigonometry Formulas and identities** that you have to learn. These Ratios and identities are very useful in solving Trigonometric problems.

**Trigonometry formulas in class 10th** are based on **Trigonometric ratios.** There are three main Trigonometric formulas for class 10th and using these three you can make other identities.

1) cos^{2} A + sin^{2} A = 1.

- a) cos
^{2}A =1 – sin^{2}A. - b) sin
^{2}A =1 – cos^{2}A.

2) 1 + tan^{2} A = sec^{2} A.

- a) sec
^{2}A – tan^{2}A = 1. - b) tan
^{2}A = sec^{2}A – 1.

3) cot^{2} A + 1 = cosec^{2} A.

- a) cosec
^{2}A – cot^{2}A = 1. - b) cot
^{2}A = cosec^{2}A – 1.

Two more **Trigonometric formulas for class 10** are there:-

(i)sec A – tan A =1/(sec A + tan A)

(ii) cosec A – cot A = 1/(cosec A + cot A)

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