PPT: Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


TRIGONOMETRIC 
FUNCTIONS
Page 2


TRIGONOMETRIC 
FUNCTIONS
Introduction
Origins
'Trigonometry' comes from 
Greek words 'trigon' (triangle) 
and 'metron' (measure). It 
began as a way to measure 
triangles.
Historical Uses
Sea captains used it for 
navigation. Surveyors mapped 
new lands with it. Engineers 
applied it to solve real-world 
problems.
Modern Applications
T oday, trigonometry helps in 
seismology, electric circuits, 
quantum physics, tide 
prediction, and music analysis.
Page 3


TRIGONOMETRIC 
FUNCTIONS
Introduction
Origins
'Trigonometry' comes from 
Greek words 'trigon' (triangle) 
and 'metron' (measure). It 
began as a way to measure 
triangles.
Historical Uses
Sea captains used it for 
navigation. Surveyors mapped 
new lands with it. Engineers 
applied it to solve real-world 
problems.
Modern Applications
T oday, trigonometry helps in 
seismology, electric circuits, 
quantum physics, tide 
prediction, and music analysis.
Angles
What is an Angle?
An angle is the rotation of a 
ray around its fixed endpoint, 
from an initial side to a 
terminal side.
Positive vs Negative
Angles are positive when 
rotating counterclockwise 
and negative when 
clockwise.
Units of Measurement
Angles are measured in 
revolutions, degrees, or 
radians, each serving specific 
mathematical purposes.
Page 4


TRIGONOMETRIC 
FUNCTIONS
Introduction
Origins
'Trigonometry' comes from 
Greek words 'trigon' (triangle) 
and 'metron' (measure). It 
began as a way to measure 
triangles.
Historical Uses
Sea captains used it for 
navigation. Surveyors mapped 
new lands with it. Engineers 
applied it to solve real-world 
problems.
Modern Applications
T oday, trigonometry helps in 
seismology, electric circuits, 
quantum physics, tide 
prediction, and music analysis.
Angles
What is an Angle?
An angle is the rotation of a 
ray around its fixed endpoint, 
from an initial side to a 
terminal side.
Positive vs Negative
Angles are positive when 
rotating counterclockwise 
and negative when 
clockwise.
Units of Measurement
Angles are measured in 
revolutions, degrees, or 
radians, each serving specific 
mathematical purposes.
Degree Measure
1°
Degree
One degree equals 1/360 of a 
complete revolution around a 
circle.
60'
Minutes
Each degree divides into 60 
minutes, written as 60' .
60
Seconds
Each minute divides into 60 
seconds, written as 60" .
Page 5


TRIGONOMETRIC 
FUNCTIONS
Introduction
Origins
'Trigonometry' comes from 
Greek words 'trigon' (triangle) 
and 'metron' (measure). It 
began as a way to measure 
triangles.
Historical Uses
Sea captains used it for 
navigation. Surveyors mapped 
new lands with it. Engineers 
applied it to solve real-world 
problems.
Modern Applications
T oday, trigonometry helps in 
seismology, electric circuits, 
quantum physics, tide 
prediction, and music analysis.
Angles
What is an Angle?
An angle is the rotation of a 
ray around its fixed endpoint, 
from an initial side to a 
terminal side.
Positive vs Negative
Angles are positive when 
rotating counterclockwise 
and negative when 
clockwise.
Units of Measurement
Angles are measured in 
revolutions, degrees, or 
radians, each serving specific 
mathematical purposes.
Degree Measure
1°
Degree
One degree equals 1/360 of a 
complete revolution around a 
circle.
60'
Minutes
Each degree divides into 60 
minutes, written as 60' .
60
Seconds
Each minute divides into 60 
seconds, written as 60" .
Radian Measure
Unit Circle
One radian equals the angle 
subtended at the center by an 
arc of length 1 in a unit circle.
Arc Length
In a circle of radius r, an arc of 
length r subtends an angle of 1 
radian.
Relationship
For an arc of length l in a circle of 
radius r, the angle » in radians is: 
» = l/r