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NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Q1: Find the radian measures corresponding to the following degree measures:
(i) 25°
(ii) – 47° 30'
(iii) 240°
(iv) 520°
Ans:
(i)  25°

       We know that 180° = π radian

       NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(ii) –47° 30'
= NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  degree [1° = 60']
NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functionsdegree
Since 180° = π radian
NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(iii) 240°
We know that 180° = π radian
NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(iv) 520°
We know that 180° = π radian
NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Q2: Find the degree measures corresponding to the following radian measuresNCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .
(i) NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  
(ii) – 4
(iii) NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions    
(iv) NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
Ans: (i) 11/16
We know that π radian = 180°

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(ii) – 4
We know that π radian = 180°

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(iii) NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
We know that π radian = 180°

      NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(iv) NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
We know that π radian = 180°

     NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Q3: A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Ans: Number of revolutions made by the wheel in 1 minute = 360
∴ Number of revolutions made by the wheel in 1 second = NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
In one complete revolution, the wheel turns an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e., 12 π radian
Thus, in one second, the wheel turns an angle of 12π radian.

Q4: Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric FunctionsAns: We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Therefore, for r = 100 cm, l = 22 cm, we have

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Thus, the required angle is 12°36′.

Q5: In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Ans:  Diameter of the circle = 40 cm                                                                                  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

∴Radius (r) of the circle = NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
Let AB be a chord (length = 20 cm) of the circle.
In ΔOAB, OA = OB = Radius of circle = 20 cm
Also, AB = 20 cm
Thus, ΔOAB is an equilateral triangle.
∴ θ = 60° = NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
Thus, the length of the minor arc of the chord is NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

Q6: If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Ans: Let the radii of the two circles be  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions   and  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions   . Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r1, while let an arc of length subtend an angle of 75° at the centre of the circle of radius r2.
Now, 60° = NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions and 75° = NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Thus, the ratio of the radii is 5:4.

Q7: Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm  
(ii) 15 cm         
(iii) 21 cm
Ans: We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .
It is given that r = 75 cm
(i) Here, l = 10 cm

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions
(ii) Here, = 15 cm

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

(iii) Here, = 21 cm

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

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FAQs on NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

1. What are the basic trigonometric functions?
Ans. The basic trigonometric functions are sine, cosine, and tangent, which relate the angles of a triangle to the lengths of its sides.
2. What is the unit circle and its relation to trigonometric functions?
Ans. The unit circle is a circle with a radius of 1 centered at the origin on the coordinate plane. It is used to define the values of trigonometric functions for all angles.
3. How can trigonometric functions be used to solve real-life problems?
Ans. Trigonometric functions can be used to solve problems involving angles and distances, such as calculating the height of a building or the distance between two points.
4. What is the reciprocal relationship between trigonometric functions?
Ans. The reciprocal relationship between trigonometric functions refers to the fact that the sine, cosine, and tangent functions are reciprocals of each other. For example, the cosecant of an angle is the reciprocal of the sine of that angle.
5. How can trigonometric functions be used in calculus and physics?
Ans. Trigonometric functions are essential in calculus for solving integrals and differential equations involving trigonometric expressions. In physics, they are used to analyze periodic phenomena such as waves and oscillations.
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