1.
By ;- Soumyadeepta Roy
Class:- XI ‘B’
Roll no:- 31

2.
INTRODUCTION
The word trigonometry is derived
from the Greek words ‘trigon’ and
‘metron’ and it means ‘measuring the
sides of a triangle’
If in a circle of radius ‘ r ’, an arc of
length ‘ l ’ subtends an angle of
radians, then l = r

3.
INTRODUCTION
 What about angles greater than 90°? 180°?
 The trigonometric functions are defined in terms of a
point on a terminal side
 r is found by using the Pythagorean Theorem:
22
yxr 

4.
RELATION BETWEEN
DEGREE AND RADIUS
1 radian= 180°/╥ =57°16’
1° = ╥/180 radian

5.
THE 6 TRIGONOMETRIC FUNCTIONS OF
ANGLE  ARE:
sin
y
r
 
cos 
tan  ,
sin 
0
0
0
csc ,
sec ,
cot ,
r
y
y
r
x
x
x
y
y
  
  
  0x 

6.
THE TRIGONOMETRIC FUNCTIONS
 The trigonometric values do not depend on the selected
point – the ratios will be the same:

7.
First Quadrant:
sin  = +
cos  = +
tan  = +
cosec  = +
sec  = +
cot  = +

8.
y
x

9.
y
x

10.
ALL STAR TRIG CLASS
 Use the phrase “All Star Trig Class” to
remember the signs of the trig functions in
different quadrants:
AllStar
Trig Class
All functions
are positive
Sine is positive
Tan is positive Cos is positive

11.
The value of any trig function of an angle  is equal to
the value of the corresponding trigonometric function of
its reference angle, except possibly for the sign. The
sign depends on the quadrant that  is in.
So, now we know the signs of the trig
functions, but what about their values?...

12.
REFERENCE ANGLES
 The reference angle, α, is the angle between the
terminal side and the nearest x-axis:

13.
ALL STAR TRIG CLASS
 Use the phrase “All Star Trig Class” to
remember the signs of the trig functions in
different quadrants:
AllStar
Trig Class
All functions
are positive
Sine is positive
Tan is positive Cos is positive

14.
TRIGONOMETRIC IDENTITIES
 Reciprocal Identities
1
sin
csc
x
x

1
cos
sec
x
x

1
tan
cot
x
x

sin
tan
cos
x
x
x

cos
cot
sin
x
x
x

Quotient Identities

15.
QUADRATIC ANGLES
(TERMINAL SIDE LIES ALONG AN AXIS)

16.
THE VALUE OF TRIGONOMETRIC
FUNCTIONS FOR SOME COMMON
ANGLES.
0˚ ╥/6 ╥/4 ╥/3 ╥/2 ╥ 3╥/2 2
╥
0
½ 1/ 2 3 /2 1 0 -1 0
1 3 /2 1/ 2
½ 0 -1 0 1
0 1/ 3 1 3 Not
defined
0 Not
defined
0
sin
cos
tan

17.
TRIGONOMETRIC IDENTITIES
2 2
1sin cosx x 
2 2
1 cot cscx x 
2 2
1tan secx x 
 Pythagorean Identities
 The fundamental Pythagorean identity:
 Divide the first by sin2x :
 Divide the first by cos2x :

18.
TRIGONOMETRIC IDENTITIES

19.
TRIGONOMETRIC IDENTITIES

20.
THANK
YOU