ত্রিকোণমিতির সূত্র সমূহ

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
Angles (In Radians)	0°	π/6	π/4	π/3	π/2	π	3π/2	2π
sin	0	1/2	1/√2	√3/2	1	0	-1	0
cos	1	√3/2	1/√2	1/2	0	-1	0	1
tan	0	1/√3	1	√3	∞	0	∞	0
cot	∞	√3	1	1/√3	0	∞	0	∞
cosec	∞	2	√2	2/√3	1	∞	-1	∞
sec	1	2/√3	√2	2	∞	-1	∞	1

Quadrant

Quadrants→	I	II	III	IV
Sin A	+	+	–	–
Cos A	+	–	–	+
Tan A	+	–	+	–
Cot A	+	–	+	–
Sec A	+	–	–	+
Cosec A	+	+	–	–

Quadrant I

• sin(π/2−θ) = cos θ

• cos(π/2−θ) = sin θ

• tan(π/2−θ) = cot θ

• cot(π/2−θ) = tan θ

• sec(π/2−θ) = cosec θ

• cosec(π/2−θ) = sec θ

 

 

Quadrant II

 

 

• sin(π−θ) = sin θ

• cos(π−θ) = -cos θ

• tan(π−θ) = -tan θ

• cot(π−θ) = – cot θ

• sec(π−θ) = -sec θ

• cosec(π−θ) = cosec θ

 

 

Quadrant III

 

• sin(π+ θ) = – sin θ

• cos(π+ θ) = – cos θ

• tan(π+ θ) = tan θ

• cot(π+ θ) = cot θ

• sec(π+ θ) = -sec θ

• cosec(π+ θ) = -cosec θ

 

Quadrant IV

 

 

• sin(2π− θ) = – sin θ

• cos(2π− θ) = cos θ

• tan(2π− θ) = – tan θ

• cot(2π− θ) = – cot θ

• sec(2π− θ) = sec θ

• cosec(2π− θ) = -cosec θ

আবার,

 

• sin(2nπ + θ ) = sin θ

• cos(2nπ + θ ) = cos θ

• tan(2nπ + θ ) = tan θ

• cot(2nπ + θ ) = cot θ

• sec(2nπ + θ ) = sec θ

• cosec(2nπ + θ ) = cosec θ

 

 

১। cosec θ = 1/sin θ

২। sec θ = 1/cos θ

৩। cot θ = 1/tan θ

৪। sin θ = 1/cosec θ

৫। cos θ = 1/sec θ

৬। tan θ = 1/cot θ

৭। sinθ=1/cosecθ

৮। cosecθ=1/sinθ

৯। cosθ=1/secθ

১০। secθ=1/cosθ

১১। tanθ=1/cotθ

১২। cotθ=1/tanθ

১৩। sin²θ + cos²θ= 1

১৪। sin²θ = 1 – cos²θ

১৫। cos²θ = 1- sin²θ

১৬। sec²θ – tan²θ = 1

১৭। sec²θ = 1+ tan²θ

১৮। tan²θ = sec²θ – 1

১৯। cosec²θ – cot²θ = 1

২০। cosec²θ = cot²θ + 1

২১। cot²θ = cosec²θ – 1

২২। sin (A + B) = sin A cos B + cos A sin B

২৩। sin (A − B) = sin A cos B – cos A sin B

২৪। cos (A + B) = cos A cos B – sin A sin B

২৫। cos (A – B) = cos A cos B + sin A sin B

২৬। tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]

২৭। tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

২৮। sin2A = 2sinA . cosA

= [2tan A/(1+tan2 A)]

২৯। cos2A = cos2A–sin2A

= [(1-tan2 A) / (1+tan2 A)]

৩০। cos2A = 2cos2A−1

= 1–2sin2A

৩১। tan(2x) = [2tan(x)]/ [1−tan2(x)]

৩২। sec (2x) = sec2 x/(2-sec2 x)

৩৩। cos (2x) = (sec x. cos x)/2

৩৪। Sin 3x = 3sin x – 4sin3x

৩৫। Cos 3x = 4cos3x-3cos x

৩৬। Tan 3x = [3tanx-tan3x]/[1-3tan2x]

৩৭। sin x sin y = 1/2 [cos(x–y) − cos(x+y)]

৩৮। cos x cos y = 1/2[cos(x–y) + cos(x+y)]

৩৯। sin x cos y = 1/2[sin(x+y) + sin(x−y)]

৪০। cos x sin y = 1/2[sin(x+y) – sin(x−y)]

৪১। sin C + sin D = 2 sin [(C+D)/2] cos [(C-D)/2]

৪২। sin C – sin D = 2 cos [(C+D)/2] sin [(C-D)/2]

৪৩। cos C + cos D = 2 cos [(C+D)/2] cos [(C-D)/2]