NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 3 / TRIGONOMETRIC FUNCTIONS EX 3.1 /

Question 1. Find the radian measures corresponding to the following degree measures:

  • (i) 25°
  • (ii) -47°30′
  • (iii) 240°
  • (iv) 520°

Solution.

We have, 180° = π Radians

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 1

Question 2. Find the degree measures corresponding to the following radian measures \left( Use\quad \pi =\frac { 22 }{ 7 } \right)

  • (i) \frac { 11 }{ 16 }
  • (ii) -4
  • (iii) \frac { 5\pi }{ 3 }
  • (iv) \frac { 7\pi }{ 6 }

Solution.

We have π Radians = 180°

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 2

Question 3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second ?

Solution.

Number of revolutions made by wheel in one minute = 360

As we know that, 1 Revolution = 27 π Radians

∴ 360 Revolutions = 720 π Radians

∴ In 1 minute wheel can make = 720 π Radians

⇒ In 60 seconds wheel can make = 720 π Radians

⇒ In 1 second wheel can make

\frac { 720\pi }{ 3 } Radians=12\pi \quad Radians

Question 4. 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 \left( Use\quad \pi =\frac { 22 }{ 7 } \right)

Solution.

Let O be the centre and AB be the arc length of the circle.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 3

Question 5. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of Xhe chord.

Solution.

Let AB be the minor arc of the chord.

AB = 20 cm, OA = OB = 20 cm

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 4

Question 6. If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their, radii.

Solution.

Let r1 r2 and θ1, θ2 be the radii and angles subtended at the centre of two circles respectively.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 5

Question 7. Find the angle in radian through 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

Solution.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 6