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TRIGONOMETRYSides of Right-Angled Triangle
Relations In Trigonometric Ratios
Trigonometric Ratios Of Complementary Angles
Trigonometric Ratios Of Standard Angles
Here ND is not de�ned
Trigonometric Identities
In right-angled ∆ABC,FA is an acute angle,AC is the hypotenuse,BC is the side opposite to FA,AB is the side adjacent to FA.
sin2 A + cos2 A = 1
1 - cos2 A = sin2 A
1 - sin2 A = cos2 A
N
N
1+ tan2 A = sec2 A
sec2 A - tan2 A = 1
sec2 A - 1 = tan2 A
N
N
1+ cot2 A = cosec2 A
cosec2 A - cot2 A = 1
cosec2 A - 1 = cot2 A
N
N
1 cos A = tan A x cosec A = cot A
cosec Asec A =
1 sin A = cot A x sec A = tan A
sec ACosec A =
Angle0o
0 1 2 3 4
10
30o 45o 60o 90o
Ratio
14
12
34
10sin A 12
12√
32
√
1 0cos A 32
√ 12√
12
1 ND0tan A 3√13√
1ND 0cot A 3√ 13√
12NDcosec A 2√ 23√
2 ND1sec A 2√23√
Write values in reverse order
Find square root for all
write numbersfrom 0 to 4
Divide allby 4
Write values in reverse order
Write values in reverse order
Use
sec A = 1 cos A
Use tan A = sin A cos A
sin Acos A cosec A
sec A= =tan A = 1 cot A
sin Acos A cosec A
sec Acot A = = = 1
tan A
sin (90-A) = cos Acos (90-A) = sin A
tan (90-A) = cot Acot (90-A) = tan A
sec (90-A) = cosec Acosec (90-A) = sec A
sine and cosine are complementary to each other
tangent and cotangent are complementary to each other
cosecant and secant are complementary to each other
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Sine of FA = sin A = =hypotenuseopposite side BC
AC
Cosine of FA = cos A = =hypotenuse
adjacent side ABAC
Tangent of FA = tan A = =opposite sideadjacent side
BCAB
Cotangent of FA = cot A = =opposite sideadjacent side
BCAB
Secant of FA = sec A = =hypotenuse
adjacent sideACAB
Cosecant of FA = cosec A = =hypotenuseopposite side BC
AC
Trigonometric Ratios Of AA Side adjacent to FA
Hypotenuse
Side
opp
osite
to F
A
B
C