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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:-
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.
Now, let me make this simpler!
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.
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 as (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.
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.
2) 1 + tan^{2} A = sec^{2} A.
3) cot^{2} A + 1 = cosec^{2} A.
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)