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Maths Class 11 Chapter 3
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The amount of rotation from the initial side to the
terminal side is Called the measure of
the angle
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Measurement of Angles
There are three system for measuring angles,
1
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The symbol 1° is
used to denote one degree
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Symbols 1′ and 1″ are used to denote one
minute and one second, respectively
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ncerthelp
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e
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Centesimal System (French System)
In this system, a right angle is divided into 100 equal parts, called ‘grades’
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i
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, 1 right angle = 100 grades = 100g
1g = 100′
1′ = 100″
3
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A radian is the angle subtended at the centre of a circle by an arc, whose length is equal to the
radius of the circle
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Relationships
(i) π radian = 180°
or 1 radian (180°/π)= 57°16’22”
where, π = 22/7 = 3
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01746 rad
(iii) If D is the number of degrees, R is the number of radians and G is the number of grades in
an angle θ, then

(iv) θ = l/r where θ = angle subtended by arc of length / at the centre of the circle, r = radius of
the circle
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ncerthelp
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Taking 0 as the centre and a unit radius, draw a
circle, cutting the coordinate axes at A,B, A’ and B’, as shown in the figure
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ncerthelp
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Trigonometric Identities
An equation involving trigonometric functions which is true for all those angles for which the
functions are defined is called trigonometrical identity
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The angles — θ, 90° ± θ, 180° ± θ, 270° + θ, 360° —θ etc
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Trigonometric Periodic Functions
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A function f(x) is said to be periodic, if there exists a real number T> 0 such that f(x + T)= f(x)
for all x
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Maximum and Minimum Values of Trigonometric Expressions

Trigonometric Ratios of Compound Angles
The algebraic sum of two or more angles are generally called compound angles and the angles
are known as the constituent angle
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Transformation Formulae
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Trigonometric Ratios of Multiple Angles

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Trigonometric Ratios of Some Useful Angles

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10 | P a g e

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11 | P a g e

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