ত্রিকোণমিতির সূত্রসমূহ
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]
৪৪। cos C – cos D = -2 sin [(C+D)/2] sin [(C-D)/2]
ত্রিকোণমিতিক অনুপাত
- sinθ=लম্ব/অতিভূজ
- cosθ=ভূমি/অতিভূজ
- tanθ=लম্ব/ভূমি
- cotθ=ভূমি/লম্ব
- secθ=অতিভূজ/ভূমি
- cosecθ=অতিভূজ/লম্ব
ত্রিকোণমিতিক কোণের মান
| 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
চিহ্নের ত্রিকোণমতিক ফাংশন
-
- sin (-θ) = − sin θ
-
- cos (−θ) = cos θ
-
- tan (−θ) = − tan θ
-
- cosec (−θ) = − cosec θ
-
- sec (−θ) = sec θ
-
- cot (−θ) = − cot θ
ইনভার্স ফাংশন
- sin-1 (–x) = – sin-1 x
- cos-1 (–x) = π – cos-1 x
- tan-1 (–x) = – tan-1 x
- cosec-1 (–x) = – cosec-1 x
- sec-1 (–x) = π – sec-1 x
- cot-1 (–x) = π – cot-1 x
