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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