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Trigonometry for Bank Exam

Nov 18 • Bank, Maths Notes, question bank • 635 Views • No Comments on 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= π– 3 × 180/π = 60°

Length of arc : l = rθ

                       l = length

                       r = radius

                       θ  = angle measured in radian

Trigonometry  for Bank Exam

Trigonometric ratios

 

capture

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

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

capture

  • 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

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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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