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.

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}**

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

Angle |
0° |
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**

- sin
^{2}A + cos^{2}A = 1 - tan
^{2}A + 1 = sec^{2}A - cot
^{2}A + 1 = cosec^{2}A

**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+tan
^{2}A)] - cos2A = cos
^{2}A–sin^{2}A = 1–2sin^{2}A = 2cos^{2}A–1= [(1-tan^{2}A)/(1+tan^{2}A)] - tan2A = (2 tanA)/(1-tan
^{2}A)

**Triple Angle Formulas**

- sin3A = 3sinA – 4sin
^{3}A - cos3A = 4cos
^{3}A – 3cosA - tan3A = [3tanA–tan
^{3}A]/[1−3tan^{2}A]

- sin(90° – θ) = cosθ
- cos(90° – θ) = sinθ
- tan(90° – θ) = cotθ
- cot(90° – θ) = tanθ
- sec(90° – θ) = cosecθ
- cosec(90° – θ) = secθ
- sin
^{2}θ + cos^{2}θ = 1 - sec2θ = 1 + tan2θ for 0° ≤ θ < 90°
- Cosec2θ = 1 + cot2θ for 0° ≤ θ ≤ 90°

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.

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