The

**solutions**for the

**Trigonometric Functions**are not readily available. While many schools may have a ready-made solution for this set in their school textbook, some might not. This is where our solution will be useful. In this article, you will find detailed solutions provided by us for the above set.Trigonometric Functions (Key Concept Reference) describes some basic and advanced uses of trigonometric functions, including identities, graph transformations, inverse functions, solutions of triangles, and polar coordinates.

Ncert **Plus one Maths** chapter-wise textbook solution for **chapter 3 Trigonometric Functions** **Exercise 3.1**. It contains detailed solutions for each question which have prepared by expert teachers to make each answer easily understand the students. they are well arranged **solutions** so that students would be able to understand easily.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus One |

Subject | Math's Textbook Solution |

Chapter | Chapter 3 |

Exercise | Ex 3.1 |

Chapter Name | Trigonometric Functions |

Category | Plus One Kerala |

## Kerala Syllabus Plus One Math's Textbook Solution Chapter 3 Trigonometric Functions Exercises 3.1

### Chapter 3 Trigonometric Functions Textbook Solution

### Chapter 3 Trigonometric Functions Exercise 3.1

Find the radian measures corresponding to the following degree measures:

(i) 25° (ii) – 47° 30' (iii) 240° (iv) 520°

(i) 25°

We know that 180° = π radian

(ii) –47° 30'

–47° 30' = degree [1° = 60']

degree

Since 180° = π radian

(iii) 240°

We know that 180° = π radian

(iv) 520°

We know that 180° = π radian

Find the degree measures corresponding to the following radian measures

.

(i) (ii) – 4 (iii) (iv)

(i)

We know that π radian = 180°

(ii) – 4

We know that π radian = 180°

(iii)

We know that π radian = 180°

(iv)

We know that π radian = 180°

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

Number of revolutions made by the wheel in 1 minute = 360

∴Number of revolutions made by the wheel in 1 second =

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.

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.

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

Therefore, forr = 100 cm, l = 22 cm, we have

Thus, the required angle is 12°36′.

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

Diameter of the circle = 40 cm

∴Radius (*r*) of the circle =

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° =

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.

Thus, the length of the minor arc of the chord is.

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

Let the radii of the two circles be and. Let an arc of length *l* subtend an angle of 60° at the centre of the circle of radius *r*_{1}, while let an arc of length *l *subtend an angle of 75° at the centre of the circle of radius *r*_{2}.

Now, 60° =and 75° =

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.

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

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

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.

It is given that *r* = 75 cm

(i) Here, *l* = 10 cm

(ii) Here, *l *= 15 cm

(iii) Here, *l *= 21 cm

Find the values of other five trigonometric functions if , *x* lies in third quadrant.

Since *x *lies in the 3^{rd} quadrant, the value of sec *x* will be negative.

Find the values of other five trigonometric functions if , *x* lies in fourth quadrant.

Since *x* lies in the 4^{th} quadrant, the value of sin *x* will be negative.

Find the values of other five trigonometric functions if , *x* lies in second quadrant.

Since *x* lies in the 2^{nd} quadrant, the value of sec *x* will be negative.

∴sec *x* =

Find the value of the trigonometric function sin 765°

It is known that the values of sin *x *repeat after an interval of 2π or 360°.

### PDF Download

#### Chapter 3 Trigonometric Functions EX 3.1 Solution

#### Chapter 3 Trigonometric Functions EX 3.1 Solution- Preview

#### Plus One Math's Chapter Wise Textbook Solution PDF Download

- Chapter 1: Sets
- Chapter 2: Relations and Functions
- Chapter 3: Trigonometric Functions
- Chapter 4: Principle of Mathematical Induction
- Chapter 5: Complex Numbers and Quadratic Equations
- Chapter 6: Linear Inequalities
- Chapter 7: Permutation and Combinations
- Chapter 8: Binomial Theorem
- Chapter 9: Sequences and Series
- Chapter 10: Straight Lines
- Chapter 11: Conic Sections
- Chapter 12: Introduction to Three Dimensional Geometry
- Chapter 13: Limits and Derivatives
- Chapter 14: Mathematical Reasoning
- Chapter 15: Statistics
- Chapter 16: Probability

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