**Exercise 3.1 Trigonometric Functions**

**Question and Answers**

**Class 11 – Maths**

Class | Class 11 |

Subject | Mathematics |

Chapter Name | Trigonometric Functions |

Chapter No. | Chapter 3 |

Exercise | Exercise 3.1 |

Category | Class 11 Maths NCERT Solutions |

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

**Answer **

**Question 2 Find the degree measures corresponding to the following radian measures (Use π= 22/7 ).**

**Answer
**

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

**Answer **

No. of revolutions made by the wheel in 1 minute = 360

1 second = 360/60 = 6

The wheel turns 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 an angle of 12π radian.

**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 (Use π= 22/7 ).**

**Answer**

Here l = 22 cm and r = 100 cm

Using the formula

θ = 1/r, we have

⇒ θ = 22/100 = 11/50 rad (∵ θ = 1/r)

**Question 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.**

**Answer**

Given, diameter = 40 cm

∴ Radius CA = CB = diameter/ 2 = 40/ 2 = 20 cm

Also, chord AB = 20 cm

Now, we have all the three sides of Δ ABC

equal so, it is an equilateral triangle.

**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.**

**Answer**

Firstly, determine the radii of both circles by using the formula θ = l/ r and then find their ratio.

**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**

**Answer **

** (i) 10 cm**

**(i)** In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,

then θ = l /r

r = 75 cm , l = 10 cm

θ = 10/75 radian

θ = 2/15 radian

**(ii) 15 cm**

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,

then θ = l /r

r = 75 cm , l = 15 cm

θ = 15/75 radian

θ = 1/15 radian

** (iii) 21 cm**

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,

then θ = l /r

r = 75 cm , l = 21 cm

θ = 21/75 radian

θ = 7/25 radian

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