Trigonometric Functions Class 11 Topics
The topics and subtopics covered in trigonometric functions class 11
include:
Introduction
Angles
Trigonometric Functions
Trigonometric Functions of Sum and Difference of Two Angles
Introduction to Trigonometry
The word “ Trigonometry” is derived from the Greek word “trigon” and
“metron”, which means measuring the sides of a triangle. Trigonometry is a
branch of Mathematics which helps to study the relationship between the
angles and side lengths of a right triangle. In the earlier classes, we have
learnt the different trigonometric ratios of the right triangle. In
trigonometric functions class 11, we are going to study the generalised
concepts trigonometric function and their properties.
Angles
An angle is a measure which gives the rotation of a ray about its initial
position. In other words, the measurement of an angle is the amount of
rotation performed to obtain the terminal side from the initial side. The
angle can be measured in two different ways, such as
Degree: If rotation of the ray from the initial side to the terminal side is
(1/360)th of the revolution, then the angle is considered to have a measure
of one degree (1°).
Radians: The angle subtended at the centre by an arc length of one unit in
a unit circle is considered to have a measure of 1 radian.
Relation Between Degree and Radian
As we know that the circle subtends at the centre of an angle whose radian
measures 2π, and its degree measures 360 degrees.
Hence, we get
, 2π = 360 degrees
Or
π radian = 180 degrees.
Therefore, 1 Radian = 180°/π
Hence, 1 Radian = 57°16’, approximately
Also, 1 degree can be written as
1° = π/180 radian = 0.01746 radians approximately.
Trigonometric Functions
The trigonometric functions are also called the angle functions, which
relate the angles and the ratios of the sides of a right angle triangle
Considering the unit circle, the six important trigonometric functions are
given as follows:
If “n” is an integer, then
Sin x =0 ⇒ x =nπ
Cos x = 0 ⇒ x= (2n+1)π/2
The other trigonometric functions in terms of sine and cosine functions are
given as follows:
Tan x = sin x /cos x ⇒ x≠ (2n+1)π/2
Cosec x = 1/sin x ⇒x ≠ nπ,
Sec x = 1/cos x ⇒ x≠ (2n+1)π/2
Cot x = cos x/sin x ⇒ x ≠ nπ
Sum and Difference of Two Angles
Some of the important expressions for the trigonometric functions of the
sum and difference of two angles and related expressions are given as
follows:
The topics and subtopics covered in trigonometric functions class 11
include:
Introduction
Angles
Trigonometric Functions
Trigonometric Functions of Sum and Difference of Two Angles
Introduction to Trigonometry
The word “ Trigonometry” is derived from the Greek word “trigon” and
“metron”, which means measuring the sides of a triangle. Trigonometry is a
branch of Mathematics which helps to study the relationship between the
angles and side lengths of a right triangle. In the earlier classes, we have
learnt the different trigonometric ratios of the right triangle. In
trigonometric functions class 11, we are going to study the generalised
concepts trigonometric function and their properties.
Angles
An angle is a measure which gives the rotation of a ray about its initial
position. In other words, the measurement of an angle is the amount of
rotation performed to obtain the terminal side from the initial side. The
angle can be measured in two different ways, such as
Degree: If rotation of the ray from the initial side to the terminal side is
(1/360)th of the revolution, then the angle is considered to have a measure
of one degree (1°).
Radians: The angle subtended at the centre by an arc length of one unit in
a unit circle is considered to have a measure of 1 radian.
Relation Between Degree and Radian
As we know that the circle subtends at the centre of an angle whose radian
measures 2π, and its degree measures 360 degrees.
Hence, we get
, 2π = 360 degrees
Or
π radian = 180 degrees.
Therefore, 1 Radian = 180°/π
Hence, 1 Radian = 57°16’, approximately
Also, 1 degree can be written as
1° = π/180 radian = 0.01746 radians approximately.
Trigonometric Functions
The trigonometric functions are also called the angle functions, which
relate the angles and the ratios of the sides of a right angle triangle
Considering the unit circle, the six important trigonometric functions are
given as follows:
If “n” is an integer, then
Sin x =0 ⇒ x =nπ
Cos x = 0 ⇒ x= (2n+1)π/2
The other trigonometric functions in terms of sine and cosine functions are
given as follows:
Tan x = sin x /cos x ⇒ x≠ (2n+1)π/2
Cosec x = 1/sin x ⇒x ≠ nπ,
Sec x = 1/cos x ⇒ x≠ (2n+1)π/2
Cot x = cos x/sin x ⇒ x ≠ nπ
Sum and Difference of Two Angles
Some of the important expressions for the trigonometric functions of the
sum and difference of two angles and related expressions are given as
follows:
