Trigonometry for Bank Exam

Nov 18 • Bank, Maths Notes, question bank • 1128 Views •

 

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

Question asked by Best Bank Coaching 

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

Top SSC Coaching in New Delhi

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)

Join Best Exam Preparation group on Telegram 

• 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

For More Question on Trigonometry 

Trigonometry for Bank Exam

Related Posts

« Approximation Value Question for Bank Exams Alphabet Questions and Answers for Reasoning »