Relations In Trigonometric Ratios Trigonometric Ratios Of ...

[Pages:1]TRIGONOMETRY

Side opposite to FA

Sides of Right-Angled Triangle

C

In right-angled ABC,

FA is an acute angle, AC is the hypotenuse, BC is the side opposite to FA,

Hypotenuse

AB is the side adjacent to FA.

A Side adjacent to FA B

Trigonometric Ratios Of A

1

Sine

of

FA

=

sin

A

=

opposite side hypotenuse

=

BC AC

4

Cotangent

of

FA

=

cot

A

=

adjacent opposite

side side

=

AB BC

2

Cosine

of

FA

=

cos

A

=

adjacent side hypotenuse

=

AB AC

5

Secant

of

FA

=

sec

A

=

hypotenuse adjacent side

=

AC AB

3

Tangent

of

FA

=

tan

A

=

opposite adjacent

side side

=

BC AB

6

Cosecant

of

FA

=

cosec

A

=ohpyppoostiteenusisdee=

AC BC

Relations In Trigonometric Ratios

1

tan A =

sin A cos A

=

sec A cosec

A

=

1 cot A

3

sec

A

=

cosec A cot A

=

tan

A

x

cosec

A

=

1 cos

A

2

cot

A

=

cos sin

A A

=

cosec A sec A

=

1 tan A

4

Cosec A =

sec A tan A

= cot A x sec A =

1 sin A

Trigonometric Ratios Of Complementary Angles

1 sin (90-A) = cos A 2 cos (90-A) = sin A

3 tan (90-A) = cot A 4 cot (90-A) = tan A

5 sec (90-A) = cosec A 6 cosec (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

Trigonometric Identities

1 sin A + cos A = 1 N

1 - cos A = sin A N

1 - sin A = cos A

2 1+ tan A = sec A N

sec A - tan A = 1 N

sec A - 1 = tan A

3 1+ cot A = cosec A N

cosec A - cot A = 1 N

cosec A - 1 = cot A

Trigonometric Ratios Of Standard Angles

Angle 0o

Ratio

0

0

sin A

0

cos A

1

tan A

0

cot A ND

sec A

1

cosec A ND

30o 45o

60o 90o

1

2

3

4

1 4

1 2

3 4

1

1 2

1 3

2

2

1

3

1

2 2

1 2

0

1 3

1

3 ND

3

1

1 3

0

2 3

2

2 ND

2

2

2 3

1

Here ND is not de ned

write numbers from 0 to 4

Divide all by 4

Find square root

for all

Write values in reverse order

Use

tan

A

=

sin cos

A A

Write values in reverse order

Use sec A =co1s A

Write values in reverse order

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