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 = πc/4
Conversion of radian to degree : When an angle is given in radian , we multiply it by 180/ to convert it into degree
Example: πc/3= πc – 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
- sin2 θ + cos2 θ = 1
- sec2 θ – tan2 θ = 1
- cosec2 θ – cot2 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 = cos2 θ – sin2 θ = 1 – 2 sin2 = 2 cos2 θ – 1
- tan 2 θ = 2 tan θ/ 1 – tan2 θ
- sin 3 θ = 3 sin θ – 4 sin2 θ
- cos 3 θ = 4 cos3 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 = b2 + c2 – a2/2bc
- cos B = c2 + a2 – b2/2ca
- cos C = b2 + a2 – c2/2ab
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