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Trigonometry Table-
Hello friends, here you will get to see all the important questions of trigonometry and all their concepts and they will prove useful in the examination, so let us see all the formulas of trigonometry and all the questions formed from its concepts.
Right Angle Triangle-
H²= P² + B²
P² = H² – B²
B² = H² – P² HERE, P = PERPENDICULAR
H = HYPOTENUS
B = BASE
PYTHAGOREAN TRIPLET-
* A “Pythagorean Triplet” is a set of positive integers a, b and c that fits the rule a²+b² = c²
* Triplet is in the form of a²-b², 2ab, a² + b²
* Some example of Basic Pythagorean triplet –
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
(8, 15,17)
(9, 40, 41)
(11, 60, 61)
(12, 35, 37)
(13, 84, 85)
(16,63, 65)
(20, 21, 29
(28, 45, 53)
(33, 56, 65)
(36, 77, 85)
(39, 80, 89)
(48, 55, 73)
(65, 72, 97)
(20, 99, 101)
TRIGNOMETRIC FUNCTIONS-
Sinθ = P/H = लंब/कर्ण
Cosθ = B/H = आधार/कर्ण
Tanθ = P/B = लंब/आधार
Cotθ = B/P = आधार/लंब
Secθ = H/B = कर्ण/आधार
Cosecθ = H/P = कर्ण/लंब
IMPORTANT FORMULA-
Sinθ = 1/cosecθ
Cosec = 1/sinθ
Cosθ = 1/secθ
Secθ = 1/cosθ
Tanθ = 1/cotθ
Cotθ = 1/tanθ
Tanθ = sinθ/cosθ
Cotθ = cosθ/sinθ
SQUARE RELATED FORMULAE-
Sin²θ + Cos²θ = 1
Sin²θ = 1 – Cos²θ
Cos²θ = 1 – Sin²θ
Sec²θ – tan²θ = 1
Sin²θ = 1+ tan²θ
Tan²θ = sec²θ – 1
Cosec²θ – Cot²θ = 1
Cosec²θ = 1 + Cot²θ
Cot²θ = Cosec²θ – 1
sinθ/1+cosθ = 1-cosθ/sinθ
Cosθ/1-sinθ = 1+sinθ/cosθ
Tanθ/secθ+1 = secθ-1/tanθ-1
(secθ + tanθ) (secθ – tanθ) = 1
(Secθ – tanθ) = 1/secθ + tanθ
(Cosecθ + cotθ) ( cosecθ – cotθ) = 1
Cotθ/cosecθ+1 = cosecθ – 1/cotθ
Sin⁶θ + cos⁶θ = 1 – 3sin²θcos²θ
Sin⁴θ + cos⁴θ = 1-2sin²θcos²θ
Sec⁴θ + tan⁴θ = 1 + 2sec²θtan²θ
Sec⁶θ – tan⁶θ = 1 + 3sec²θtan²θ
Cosec⁴θ + Cot⁴θ = 1 + 2cosec²cot²θ
Cosec⁴θ – cot⁶θ = 1 + 3cosec²θcot²θ
TRIGONOMETRY TABLE-
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TRIGONOMETRY TABLE
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IMPORTANT CONCEPT-
CotA + tanA = 1/sinACosA = secAcosA = 2cosec2A
a/b =c/d —- a+b/a-b = c+d/c-d
If A + B = 90⁰
Then
sin A = CosB & SinA.SecB=1
Tan A = Cot B & TanA.TanB = 1 & CotA.CotB=1
Sec A = Cosec B & CosA.CosecB=1
sin²A + sin²B = 1
cos²A + cos²B = 1
CONCEPT OF DEGREE-
* Π radian = 180 degree
* 1 degree = 60 minute angle
1 minute angle = 60 second angle
1 radian = 57 degree 16 minute 22 second.
* Length of arc = radius of circle * angle in radian
Length of arc is directly proportional to radius of circle.
FORMULA OF TRIGONOMETRY-
* Sin(A+B) = sinA cosB + cosa sinB
* Sin(A-B) = sinA cosB – cosa sinB
– Cos (A+B) = CosA cosB – sinA sinB
* Cos(A-B) = cosa cosB + sinAsinB
* 2sin A *cos B = sin(A + B) + sin(A – B)
2 cosAsinB= sin(A + B) – sin(A – B)
2cosAcosB = cos(A+B) + cos(A-B)
2sinAsinB = cos(A-B) -cos(A+B)
Sin(A + B) * sin(A – B) = sin²A – sin²B =cos²B-cos² )
Cos(A+B). cos(A + B) – cos^2 A – sin^2 B = cos^2 B – sin^2 i
CONCEPT BASED ON SEC, COS, TAN, COT –
sec²A- tan²= 1
sec²A= 1 + tan²A
tan²= sec²-1
Cosec²A – cot²A = 1
cosec²A = 1 + cot²A
cot²A= cosec²A- 1
(secA- tanA) = 1/(secA + tan A)
IMPORTANT FORMULAS BASED ON C & D-
sin C + sin D = 2sin((c + D)/2) * cos((c – D)/2)
sin C – sin D = 2cos((c + D)/2) * sin((c – D)/2)
+ cos C + cos D = 2cos((c + D)/2) * cos((c – D)/2)
cos C – cos D = 2sin((c + D)/2) * sin((D – c)/2)
MANY TIME ASKED FORMULAS-
Tan(A + B) = (tan A + tan B)/(1 – tan A * tan B)
tan(A – B) = (tan A – tan B)/(1 + tan A * tan B)
Cot (A + B) = (cot A * cot B – 1)/(cot B + cot A)
Cot (A – B) = (cot A * cot B + 1)/(cot B – cot A)
sin 3A = 3sin A – 4sin^3 A
cos 3A = 4cos^3 A – 3cos A
SOME OTHER FORMULAS-
SinASin(60° – A) Sin(60°+ A) = = 1\4Sin3A
cos Acos(60-A) * cos(60+ A) = 1/4 * cos3A
tanAtan(60-A) * tan(60 + A) = tan3A
Cos²A+ Cos²(60° − A) +Cos² (60° + A) = 3/2
Cos³ + Cos³ (120° – θ) +Cos³(120°+θ)=3/4Cos3θ
tan(A + B + C) = (tan A + tan B + tan C – tan A * tan B * tan C)/(1 – tan A * tan B – tan B * tan C – tan C * tan A)
If A + B = 45 deg * or * 225 deg
then (1 + tan A)(1 + tan B) = 2
If A + B = 45 deg * or * 225 deg
then (1 – cot A)(1 – cot B) = 2
If A + B + C = 90 deg
Then anA * tan B + tan B * tan C + tan C * tan A = 1 & cot A cot B cot C = cot A + cot B + cot C
If A + B + C = 180 deg
then tan A + tan B + tan C = tan A tan B tan C aleph cot A * cot B + cot B * cot C + cot C * cot A = 1
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