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# 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= π– 3 × 180/π = 60°

Length of arc : l = rθ

l = length

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<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 θcot2 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 ) = 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 sinθ
• 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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