## Trigonometry for Bank Exam

# Trigonometry for Bank Exam

Trigonometry for Bank Exam IBPS and other government exams.

**Trigonometry **

**Angles : **The amount of turn between two straight lines that have a common point is called angles.

Generally angles are measured in degree or radian

1 degree = 60 minutes

1 minutes = 60 seconds

Suppose an angle is given as 45°23’53’’ , we read it as 45 degree 23 minutes and 53 seconds

**Conversion of degree to radian** : when an angle is given in degree, we multiply it by /180 to convert it into radian

Example : 45° = 45° × π/180 = π^{c}/4

**Conversion of radian to degree :** When an angle is given in radian , we multiply it by 180/ to convert it into degree

Example: π^{c}/3= π^{c }– 3 × 180/π = 60°

**Length of arc :** l = rθ

l = length

r = radius

θ = angle measured in radian

## Trigonometry for Bank Exam

**Trigonometric ratios**

sinθ = P/H cosecθ = H/P

cosθ = B/H secθ = H-P

tanθ = P/B cotθ = B/P

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**Table for commonly used trigonometric ratios**

0° | 30° | 45° | 60° | 90° | |

sinθ | √0/4 = 0 | √1/4 = 1/2 | √2/4 = 1/√2 | √3/4 = √3/2 | √4/4 = 1 |

cosθ | 1 | √3/2 | 1/√2 | 1/2 | 0 |

tanθ | 0 | 1/√3 | 1 | √3 | Not defined |

cosecθ | Not defined | 2 | 2 | 2/√3 | 1 |

secθ | 1 | 2/√3 | √2 | 2 | Not defined |

cotθ | Not defined | √3 | 1 | 1/√3 | 0 |

**Coordinate plane**

- In the first quadrant (0<θ<90), all trigonometric ratios are positive
- In the 2nd quadrant (90<θ<180), only sinθ and cosecθ are positive
- In the 3rd quadrant (180<θ<270), only tanθ and cotθ are positive
- In the 4th quadrant (270<θ<360), only cosθ and secθ are positive

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**Commonly used trigonometric identities**

- Sin (90 – θ) = cos θ
- Cos (90 – θ) = sin θ
- tan(90 – θ) = cot θ
- cot(90 – θ) = tan θ
- sec(90 – θ) = cosec θ
- cosec(90 – θ) = sec θ

- sinθ × cosecθ = 1
- cosθ × secθ = 1
- tanθ × cotθ = 1

- sinθ = 1/ cosec θ
- cosθ = 1/ secθ
- tanθ = sinθ/cosθ
- cotθ = cos θ / sin θ

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

- sin (- θ) = – sin θ
- cos (- θ) = cos θ
- tan (- θ) = – tan θ
- cot (- θ) = – cot θ
- cosec (- θ) = – cosec θ
- sec (- θ) = sec θ

- Sin(θ +φ ) = sinθ cosφ + sinφ cosθ
- Sin( θ– φ ) = sinθ cosφ – sin cosθ
- cos( θ+φ ) = cos θsinφ – cosφ sinθ
- cos( θ – φ ) = cosθ sinφ + cosφ sinθ
- tan( θ + φ ) = (tanθ + tanφ) / (1 – tanθ tanφ)
- tan( θ – φ ) = (tanθ – tanφ) / (1 + tanθ tanφ)

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- Sin 2 θ = 2 sinθ cosθ
- cos 2 θ = cos
^{2}θ – sin^{2}θ = 1 – 2 sin^{2}= 2 cos^{2}θ – 1 - tan 2 θ = 2 tan θ/ 1 – tan
^{2}θ

- sin 3 θ = 3 sin θ – 4 sin
^{2 }θ - cos 3 θ = 4 cos
^{3}θ – 3 cos θ

- sin A + sin B = 2 sin (A + B/2) cos(A – B/2)
- sin A – sin B = 2 cos (A + B.2) sin(A -B/2)
- cos A + cos B = 2 cos (A + B.2) cos(A -B/2)
- cos A – cos B = – 2 sin (A + B/2) sin(A -B/2)

**Sine law**

sin A/a = sin B/b = sin C/c

**Cosine law**

- cos A = b
^{2}+ c^{2}– a^{2}/2bc - cos B = c
^{2}+ a^{2}– b^{2}/2ca - cos C = b
^{2}+ a^{2}– c^{2}/2ab

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