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Topics: Trigonometry, Trigonometric functions, Euler's formula Pages: 18 (779 words) Published: November 7, 2013
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

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2
8

Values of Trigonometric ratios:


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


2



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

+



+



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3
11.

Behavior of Trigonometric Functions in various Quadrants

I quadrant
sin

cos

tan

cot

sec

cosec

12.

II quadrant

III quadrant

IV quadrant

increases from

decreases from

decreases from

increases from

0 to 1

1 to 0

0 to –1

–1 to 0

decreases from

decreases from

increases from

increases from

1 to 0

0 to –1

–1 to 0
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