Trigonometric Formulas For Class 10

Trigonometry is one of the major parts of Mathematics which deals with functions of angles and how they are calculated and used for other measurements. Trigonometry is introduced to students in CBSE class 10. Students are always advised to be fluent and should be thorough with these questions as they are very important from the exam point of view. Trigonometry has a weightage of 12 marks in the 10th board exam. 

The six functions of trigonometry are:

  • Sine
  • Cosine
  • Tangent
  • Cotangent 
  • Secant
  • Cosecant 

Trigonometry plays the most vital role in almost all the fields whether its aviation, physics, criminology, military, marine biology, development of sound waves, satellite navigation, medical imaging, etc. 

List of Class 10 Trigonometric Formulas

To find the angles or the sides of the right-angled triangle, trigonometry is used.

The trigonometric formulas are based on the three sides of a right-angled triangle, having hypotenuse (the longest side), base (adjacent side), height (opposite side), and angle θ.  

If we apply the Pythagoras theorem for the right-angled triangle, we have:

(Perpendicular)2 + (Base)2 = (Hypotenuse)2 ⇒ (P)2 + (B)2 = (H)2

Basic Trigonometric formulas

  • sin A - Perpendicular/Hypotenuse
  • cos A - Base/Hypotenuse
  • tan A - Perpendicular/Base
  • cot A - Base/Perpendicular
  • cosec A - Hypotenuse/Perpendicular
  • sec A -  Hypotenuse/Base

Trignometry Table

Angle 30° 45° 60° 90°
Sinθ 0 1/2 1/√2 √3/2 0
Cosθ 1 √3/2 1/√2 1/2 1
Tanθ 0 1/√3 1 √3 0
Cotθ Undefined √3 1 1/√3 Undefined
Secθ 1 2/√3 √2 2 1
Cosecθ Undefined 2 √2 2/√3 Undefined

Reciprocal Relation Between Trigonometric Ratios

  • tanA - sinA/cosA
  • cotA - cosA/sinA
  • cosecA - 1/sinA
  • secA - 1/cosA

Trigonometric Sign Functions

  • sin(-θ) = −sin θ
  • cos(−θ) = cos θ
  • tan(−θ) = −tan θ
  • cosec(−θ) = −cosec θ
  • sec(−θ) = sec θ
  • cot(−θ) = −cot θ

Trigonometric Identities

  • sin2A + cos2A = 1
  • tan2A + 1 = sec2A
  • cot2A + 1 = cosec2A

Periodic Identities

  • sin(2nπ + θ) = sinθ
  • cos(2nπ + θ) = cosθ
  • tan(2nπ + θ) = tanθ
  • cot(2nπ + θ) = cotθ
  • sec(2nπ + θ) = secθ
  • cosec(2nπ + θ) = cosecθ

Complementary Ratios

        Quadrant I

  • sin(π/2−θ) = cosθ
  • cos(π/2−θ) = sinθ
  • tan(π/2−θ) = cotθ
  • cot(π/2−θ) = tanθ
  • sec(π/2−θ) = cosecθ
  • cosec(π/2−θ) = secθ

     Quadrant II

  • sin(π−θ) = sinθ
  • cos(π−θ) = -cosθ
  • tan(π−θ) = -tanθ
  • cot(π−θ) = -cotθ
  • sec(π−θ) = -secθ
  • cosec(π−θ) = cosecθ

     Quadrant III

  • sin(π+ θ) = – sinθ
  • cos(π+ θ) = – cosθ
  • tan(π+ θ) = tanθ
  • cot(π+ θ) = cotθ
  • sec(π+ θ) = -secθ
  • cosec(π+ θ) = -cosecθ

     Quadrant IV

  • sin(2π− θ) = – sinθ
  • cos(2π− θ) = cosθ
  • tan(2π− θ) = – tanθ
  • cot(2π− θ) = – cotθ
  • sec(2π− θ) = secθ
  • cosec(2π− θ) = -cosecθ

Sum and Difference of Two Angles

  • sin (A + B) = sin A.cos B + cos A.sin B
  • sin (A − B) = sin A.cos B – cos A.sin B
  • cos (A + B) = cos A.cos B – sin A.sin B
  • cos (A – B) = cos A.cos B + sin A.sin B
  • tan(A+B) = [(tan A + tan B)/(1 – tan A.tan B)]
  • tan(A-B) = [(tan A – tan B)/(1 + tan A.tan B)]

Double Angle Formulas

  • sin2A = 2sinA.cosA = [2tanA + (1+tan2A)]
  • cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
  • tan2A = (2 tanA)/(1-tan2A)

Triple Angle Formulas

  • sin3A = 3sinA – 4sin3A
  • cos3A = 4cos3A – 3cosA
  • tan3A = [3tanA–tan3A]/[1−3tan2A]

Some other trigonometric formulas:

  • sin(90° – θ) = cosθ
  • cos(90° – θ) = sinθ
  • tan(90° – θ) = cotθ
  • cot(90° – θ) = tanθ
  • sec(90° – θ) = cosecθ
  • cosec(90° – θ) = secθ
  • sin2θ + cos2θ = 1
  • sec2θ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosec2θ = 1 + cot2θ for 0° ≤ θ ≤ 90°

How to prepare with CREST Champs for Class 10 Maths CBSE Exam?

Formulas play an important role to score well in the class 10 CBSE Maths examination. But, only memorizing formulas alone will not help you to get good grades in Maths subject. You should have command over concepts. To ensure stronghold over concepts one can take CBSE class 10 Maths course with CREST Champs. 

CREST Champs provides year-long as well as many other CBSE Maths class 10 preparation courses. The platform offers both group as well as 1-1 classes. 

You could find the best course providers both in academics and non-academic with us.

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