Right Angle Triangle
One angle is 90°
Pythagorean Triplet:-
A “ Pythagorean Triplet” is a set of positive integers a, b and c
that fits the rule
Triplet is in the form of
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)
Trigonometric functions-
Formula:-
Formula-
Formula
Formula
Trigonometry Table
Angles 0 30 45 60 90
Ratios
Sin 0 1 1 3 1
2 2 2
1
Cos 1 3 1 0
2
2 2
Tan 0 1 1 3
3
Cosec 2 2 2 1
3
Sec 1 2 2 2
3
Cot 3 1 1 0
3
Important Concept
Angles rule
Quadrant Formula
Concept
If A + B = 90°
Then
Sin A = Cos B & SinA.SecB=1
Tan A = Cot B & TanA.TanB =1 & CotA.CotB=1
Sec A = Cosec B & CosA.CosecB=1
Range of Trigonometric ratio
Concept of degree
∏ radian = 180 degree
1 degree = 60 minute angle
1 minute angle = 60 second angle
1 radian = 57 degree 16 minute 22 second
To convert radian in to degree we multiply radian to 180.
To convert degree in to radian we multiply degree to
∏/180.
Length of arc = radius of circle * angle in radian
Length of arc is directly proportional to radius of circle.
Concept based on sin and cos
If
Then
If
If
Then
Concept based on sec, tan
cosec , cot
Concept
If
Then
If
Then
Important concept
for value putting
When we put the value of angle then the result is not in the form of 0/0, 1/0
or undefined.
We put the value of angle 0, 30, 45, 60, 90……..
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
2sinAcosB = sin(A+B) + sin (A-B)
2cosAsinB = sin(A+B) – sin(A-B)
2cosAcosB = cos(A+B) + cos(A-B)
2sinAsinB = cos(A-B) –cos(A+B)
Formula
sinC + sinD = 2sin C + D cos C − D
2 2
sinC – sinD = 2cos C + D sin C − D
2 2
cosC + cosD = 2cos C + D cos C − D
2 2
cosC – cosD = 2sin C + D sin D − C
2 2
Important Formula
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
Some Other value of
trigonometry ratio
3 +1
sin 75 = cos15 =
2 2
3 −1
sin 15 = cos 75 =
2 2
3 +1
cot 15 = tan 75 = = 2+ 3
3 −1
3 −1
cot 75 = tan 15 = = 2− 3
3 +1
Important Concept
tan A + tan B + tan C − tan A tan B tan C
If A + B = 45or 225 tan( A + B + C ) =
1 − tan A tan B − tan B tan C − tan C tan A
then(1 + tan A)(1 + tan B ) = 2
If A + B = 45or 225
then(1 − cot A)(1 − cot B ) = 2
If A + B + C = 90
Then tan A 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
then tan A + tan B + tan C = tan A tan B tan C
& cot A cot B + cot B cot C + cot C cot A = 1
