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Trigonometry All Formulas PDF – In today’s Content, we will know all the Trigonometry or Trigonometry formulas (All Trigonometry formulas in Hindi & English). Questions based on the procedure of trigonometry function are often asked in board exams or competitive exams. Basic and tricky questions based on trigonometry formulas are requested in 9th class, 10th class, 11th class, and 12th class exams.
Trigonometry Formula
Table of Trigonometry Functions (chart)
| Signal | 0° | 30 ° = π / 6 | 45 ° = π / 4 | 60 ° = π / 3 | 90 ° = π / 2 |
|---|---|---|---|---|---|
| Sinθ | 0 | ½ | 1/√2 | √3/2 | 1 |
| Cos θ | 1 | √3/2 | 1/√2 | ½ | 0 |
| Tanθ | 0 | 1/√3 | 1 | √3 | undefined |
| Cotθ | undefined | √3 | 1 | 1/√3 | 0 |
| Secθ | 1 | 2/√3 | √2 | 2 | undefined |
| Harvest | undefined | 2 | √2 | 2/√3 | 1 |
Trigonometry All Formulas PDF Trigonometry Formulas For Class 10 PDF All Formulas Of Trigonometry Class 10 All Formulas Of Trigonometry Class 11 Trigonometry Formulas For Class 11 PDF Trigonometry All Formula Class 10 Class 11 Maths Trigonometry Formulas Class 11 Trigonometry All Formulas
Basic Formulas of Trigonometry
- sinA = perpendicular hypotenuse
- cosA = base hypotenuse
- tanA = perpendicular base
- cotA = base perpendicular
- secA = hypotenuse base
- cosecA = hypotenuse
- sinA =1 cosecA
- cosA =1 secA
- tanA =1 cotA
- cotA =1 tanA
- secA =1 cosA
- cosecA =1 sinA
- tanA =sinA cosA
- cotA =cosA sinA
- sinA x cosecA = 1
- cosA x secA = 1
- tanA x cotA = 1
- sin 2 A + cos 2 A = 1
- sec 2 A – tan 2 A = 1
- cosec 2 A – cot 2 A = 1
Formulas for Measurement of Angles in Trigonometry
- radian measurement = π 180x degree measurement
- degree measurement = 180 πx radian measurement
Fundamentals of Trigonometry
- sin2x + cos2x = 1
- 1 + tan2x = sec2x
- 1 + cot2x = cosec2x
- cos (2πn + θ) = cosθ
- sin (2πn + θ) = sinθ
- sin (-θ) = -sinθ
- cos (-θ) = cosθ
Trigonometry ratio of the sum of two angles
- sin (A + B) = sinA.cosB + cosA.sinB
- cos (A + B) = cosA.cosB – sinA.sinB
- tan (A + B) = tanA + tanB 1 – tanA.tanB
- cot (A + B) = cotA.cotB – 1 cotB + cotA
More Trigonometry Formula
(A) (1) sin (π 2+ A) = cosA (2) cos (π 2+ A) = -sinA (3) tan (π 2+ A) = -cotA (4) cot (π 2+ A) = -tanA (5) sec (π 2+ A) = -cosecA (6) cosec (π 2+ A) = secA
(B) (1) sin (π + A) = -sinA (2) cos (π + A) = -cosA (3) tan (π + A) = tanA (4) cot (π + A) = cotA ( 5) sec (π + A) = -secA (6) cosec (π + A) = -cosecA
(C) (1) sin (3π 2+ A) = -cosA (2) cos (3π 2+ A) = sinA (3) tan (3π 2+ A) = -cotA (4) cot (3π 2+ A) = -tanA (5) sec (3π 2+ A) = cosecA (6) cosec (3π 2+ A) = -secA
(D) (1) sin (2π + A) = sinA (2) cos (2π + A) = cosA (3) tan (2π + A) = tanA (4) cot (2π + A) = cotA (5) sec (2π + A) = secA (6) cosec (2π + A) = cosecA
Trigonometry ratio of difference of two angles
(1) sin (A – B) = sinA.cosB – cosA.sinB
(2) cos (A – B) = cosA.cosB + sinA.sinB
(3) tan (A – B) = tanA – tanB 1 + tanA.tanB (4) cot (A – B) = cotA.cotB + 1 cotB – cotA
More Trigonometry Formula
(A) (1) sin (π 2- A) = cosA (2) cos (π 2- A) = sinA (3) tan (π 2- A) = cotA (4) cot (π 2- A) = tanA (5) sec (π 2- A) = cosecA (6) cosec (π 2- A) = secA
(B) (1) sin (π – A) = sinA (2) cos (π – A) = -cosA (3) tan (π – A) = -tanA (4) cot (π – A) = -cotA (5) sec (π – A) = -secA (6) cosec (π – A) = -cosecA
(C) (1) sin (3π 2- A) = -cosA (2) cos (3π 2- A) = -sinA (3) tan (3π 2- A) = cotA (4) cot (3π 2- A) = tanA (5) sec (3π 2- A) = -cosecA (6) cosec (3π 2- A) = -secA
(D) (1) sin (2π – A) = -sinA (2) cos (2π – A) = cosA (3) tan (2π – A) = -tanA (4) cot (2π – A) = -cotA (5) sec (2π – A) = secA (6) cosec (2π – A) = -cosecA
Two Formulas of Trigonometry
(1) sin(A + B) sin(A – B) = sin2A – sin2B
(2) cos(A + B) cos(A – B) = cos2A – sin2B
Expressing Trigonometry Ratios of Angle 2A in Terms of Angle A
(1) sin2A = 2sinA.cosB
(2) cos2A = cos 2 A – sin 2 A = 2cos 2 A – 1 = 1 – 2 sin 2 A
(3) tan2A = 2tanA 1 – tan 2 A
(4) sin2A = 2tanA 1 + tan 2 A
(5) cos2A = 1 – tan 2 A 1 + tan 2 A
Expressing Trigonometry Ratios of Angle 3A in Terms of Angle A
(1) sin3A = 3sinA – 4sin 3A
(2) cos3A = 4cos 3A – 3cosA
(3) tan3A = 3tanA – tan 3 A 1 – 3tan 2 A
sum or difference of product
(1) 2sinA.cosB = sin (A + B) + sin (A – B)
(2) 2cosA.sinB = sin (A + B) – sin (A – B)
(3) 2cosA.cosB = cos (A + B) + cos (A – B)
(4) 2sinA.sinB = cos (A – B) – cos (A + B)
Conversion of sum and difference product
(1) sinC + sinD = 2 sinC + D 2cosC – D 2
(2) sinC – sinD = 2 cosC + D 2sinC – D 2
(3) cosC + cosD = 2 cosC + D 2cosC – D 2
(4) cosC – cosD = 2 sinC + D 2sinD – C 2
General Solution of Simple Trigonometry Equations
(1) If sinθ = 0, then its general solution will be = nπ, where n is zero or any positive or negative integer, that is, n.
(2) If cosθ = 0, its general solution will be = (2n + 1)π/2, where n is zero or any positive or negative integer, that is, n.
(3) If tanθ = 0, then the general solution will be = nπ, where n is zero or any positive or negative integer, that is, n.
| Values of the functions for (180 0 + ) | Values of the functions for (270 0 – ) |
| Sin (180 0 + θ) = – Sin θCos (180 0 + θ) = – Cos θTan (180 0 + θ) = + Tan θSec (180 0 + θ) = – Sec θCot (180 0 + θ) = + Cot θCosec (180 0 + θ) = -Cosec θ | Sin (270 0 – θ) = – Cos θCos (270 0 – θ) = – Sin θTan (270 0 – θ) = + Cot θSec (270 0 – θ) = – Cosec θCot (270 0 – θ) = + Tan θCosec (270 0 -θ) = -Sec θ |
General Solution of Trigonometry Equations
(1) If sinθ = sinα then its comprehensive solution = nπ + (-1) n α ∀ n ∈ I
(2) If cosθ = cosα then its comprehensive solution = 2nπ + α, ∀ n ∈ I
(3) if tanθ = tanα then its broad solution = nπ + α, n ∈ I
Trigonometry All Formulas PDF Download Information
| Book: | Trigonometry All Formulas PDF Book |
| Subjects: | Maths |
| Language: | English, and Hindi |
| Total Pages: | 10 Pages |
| File Size: | 546 KB |
| Format: | PDF (Scanned Copy) |
| Download Source: | Google Drive |
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