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NCERT Class 11 Maths Textbook Chapter 3 With Answer Book PDF Free Download
Chapter 3: Trigonometric Functions
3.1 Introduction
The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle.
The subject was originally developed to solve geometric problems involving triangles. It was studied by sea captains for navigation, surveyor to map out the new lands, engineers, and others.
Currently, trigonometry is used in many areas such as the science of seismology, designing electric circuits, describing the state of an atom, predicting the heights of tides in the ocean, analyzing a musical tone, and many other areas.
In earlier classes, we have studied the trigonometric ratios of acute angles as the ratio of the sides of a right-angled triangle.
We have also studied the trigonometric identities and application of trigonometric ratios in solving the problems related to heights and distances.
In this Chapter, we will generalize the concept of trigonometric ratios to trigonometric functions
and study their properties.
3.2.2 Radian measure
There is another unit for measurement of an angle, called the radian measure. The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) is said to have a measure of 1 radian. In Fig 3.4(i) to (iv), OA is the initial side and OB is the terminal side.
3.2.4 Relation between degree and radian
Since a circle subtends at the center an angle whose radian measure is 2π and its degree measure is 360°, it follows that
2π radian = 360° or π radian = 180°
| Author | NCERT |
| Language | English |
| No. of Pages | 37 |
| PDF Size | 2.7 MB |
| Category | Mathematics |
| Source/ Credits | ncert.nic.in |
NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions
1. Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°
Solution:
(iv) 520°
2. Find the degree measures corresponding to the following radian measures (Use π = 22/7)
(i) 11/16
(ii) -4
(iii) 5π/3
(iv) 7π/6
Solution:
(i) 11/16
Here π radian = 180°
(ii) -4
Here π radian = 180°
(iii) 5π/3
Here π radian = 180°
We get
= 300o
(iv) 7π/6
Here π radian = 180°
We get
= 210o
3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Solution:
It is given that
No. of revolutions made by the wheel in
1 minute = 360
1 second = 360/60 = 6
We know that
The wheel turns at an angle of 2π radian in one complete revolution.
In 6 complete revolutions, it will turn an angle of 6 × 2π radian = 12 π radian
Therefore, in one second, the wheel turns at an angle of 12π radian.
4. Find the degree measure of the angle subtended at the center of a circle of radius 100 cm by an arc of length 22 cm (Use π = 22/7).
Solution:
5. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Solution:
The dimensions of the circle are
Diameter = 40 cm
Radius = 40/2 = 20 cm
Consider AB be as the chord of the circle i.e. length = 20 cm
In ΔOAB,
Radius of circle = OA = OB = 20 cm
Similarly AB = 20 cm
Hence, ΔOAB is an equilateral triangle.
θ = 60° = π/3 radian
In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the center
We get θ = 1/r
Therefore, the length of the minor arc of the chord is 20π/3 cm.
NCERT Class 11 Maths Textbook Chapter 3 With Answer Book PDF Free Download