Trigonometry Class 11th Mathematics Notes
Angle
Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and
the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex.
If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is
clockwise, then the angle is negative.
Measuring Angles
There are two systems of measuring angles
Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is (1360)th of a
revolution, the angle is said to have a measure of one degree, written as 1°.
One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written
as 1″
Thus, 1° = 60′ and 1′ = 60″
Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose
length is equal to the radius of the circle. We denote 1 radian by 1°.
Relation Between Radian and Degree
We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°.
2π radian = 360°.
Hence, π radian = 180°
or 1 radian = 57° 16′ 21″ (approx)
1 degree = 0.01746 radian
Six Fundamental Trigonometric Identities
sinx = 1cosecx
cos x = 1secx
tan x = 1cotx
sin2 x + cos2 x = 1
1 + tan2x = sec2 x
1 + cot2 x = cosec2 x
Trigonometric Functions – Class 11 Maths Notes
Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The
extension of trigonometric ratios to any angle in terms of radian measure (real number) are called
trigonometric function. The signs of trigonometric function in different quadrants have been given in
following table.
I II III IV
Sin x + + – –
Cos x + – – +
Tan x + – + –
Cosec x + + – –
Sec x + – – +
Cot x + – + –
Domain and Range of Trigonometric Functions
Angle
Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and
the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex.
If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is
clockwise, then the angle is negative.
Measuring Angles
There are two systems of measuring angles
Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is (1360)th of a
revolution, the angle is said to have a measure of one degree, written as 1°.
One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written
as 1″
Thus, 1° = 60′ and 1′ = 60″
Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose
length is equal to the radius of the circle. We denote 1 radian by 1°.
Relation Between Radian and Degree
We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°.
2π radian = 360°.
Hence, π radian = 180°
or 1 radian = 57° 16′ 21″ (approx)
1 degree = 0.01746 radian
Six Fundamental Trigonometric Identities
sinx = 1cosecx
cos x = 1secx
tan x = 1cotx
sin2 x + cos2 x = 1
1 + tan2x = sec2 x
1 + cot2 x = cosec2 x
Trigonometric Functions – Class 11 Maths Notes
Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The
extension of trigonometric ratios to any angle in terms of radian measure (real number) are called
trigonometric function. The signs of trigonometric function in different quadrants have been given in
following table.
I II III IV
Sin x + + – –
Cos x + – – +
Tan x + – + –
Cosec x + + – –
Sec x + – – +
Cot x + – + –
Domain and Range of Trigonometric Functions
