article on value education

1
Class XI: Maths
Chapter 3: Trigonometric Functions
Top Formulae
1.

1 radian =

2.

1o =

180o
= 57o16 ' approximately π π radians = 0.01746 radians approximately
180o

3.

s= r θ
Length of arc= radius × angle in radian

4.

This relation can only be used when θ is in radians π Radian measure=
× Degree measure
180
180
× Radian measure π 5.

Degree measure =

6.

Trigonometric functions in terms of sine and cosine cos ec x =

1
, x ≠ nπ, where n is any int eger sin x

s ec x = tan x =

sin x π , x ≠ (2n + 1) , where n is any int eger cos x
2

cot x =
7.

1 π , x ≠ (2n + 1) , where n is any int eger cos x
2

1
, x ≠ nπ, where n is any int eger tan x

Fundamental Trigonometric Identities sin2x + cos2x = 1
1 + tan2x = sec2 x
1 + cot2x = cosec2x

Get the Power of Visual Impact on your side
Log on to www.topperlearning.com

2
8

Values of Trigonometric ratios:
0°

sin cos 1

tan

9.

0

0

π
4
1

π
6
1
2

π
3

2

3
2
1
2

1

3

2
1

3
2
1
3

π
2

π

3π
2

2π

10

0

–1

0

0

–1

0

1

not defined 0

not defined 0

Domain and range of various trigonometric functions:

Function

Domain

Range

y = sin x

 π π
− 2 , 2 



[–1, 1]

y = cos x

0, π



[–1, 1]

 π π
 − 2 , 2  − {0}


π
0, π −  


2

y = cosec x

y = sec x

R – (–1, 1)

 π π
− 2 , 2 


( 0, π )

y = tan x y = cot x
10.

R – (–1,1)

R
R

Sign Convention

I

II

III

IV

sin x

+

+

–

–

cos x

+

–

–

+

tan x

+

–

+

–

cosec x

+

+

–

–

sec x

+

–

–

+

cot x

+

–

+

–

Get the Power of Visual Impact on your side
Log on to www.topperlearning.com

3
11.

Behavior of Trigonometric Functions in various Quadrants

I quadrant sin cos

tan

cot

sec

cosec