Mathematics
22
By ;- Soumyadeepta Roy Class:- XI ‘B’ Roll no:- 31
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Transcript of Mathematics
By ;- Soumyadeepta Roy
Class:- XI ‘B’
Roll no:- 31
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
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
RELATION BETWEEN
DEGREE AND RADIUS
1 radian= 180°/╥ =57°16’
1° = ╥/180 radian
THE 6 TRIGONOMETRIC FUNCTIONS OF
ANGLE ARE:
siny
r
cos
tan ,
sin 0
0
0
csc ,
sec ,
cot ,
ry
y
rx
x
xy
y
0x
THE TRIGONOMETRIC FUNCTIONS
The trigonometric values do not depend on the selected
point – the ratios will be the same:
First Quadrant:
sin = +
cos = +
tan = +
cosec = +
sec = +
cot = +
y
x
y
x
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 positiveSine is positive
Tan is positive Cos is positive
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?...
REFERENCE ANGLES The reference angle, α, is the angle between the
terminal side and the nearest x-axis:
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 positiveSine is positive
Tan is positive Cos is positive
TRIGONOMETRIC IDENTITIES
Reciprocal Identities
1sin
csc x
x
1cos
secx
x
1tan
cotx
x
sintan
cos
xx
x
coscot
sin
xx
x
Quotient Identities
QUADRATIC ANGLES
(TERMINAL SIDE LIES ALONG AN AXIS)
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
TRIGONOMETRIC IDENTITIES
2 2 1sin cosx x
2 21 cot cscx x 2 21tan secx x
Pythagorean Identities
The fundamental Pythagorean identity:
Divide the first by sin2x :
Divide the first by cos2x :
TRIGONOMETRIC IDENTITIES
TRIGONOMETRIC IDENTITIES
THANK
YOU
