Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th

# Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 6 - Trigonometry [Latest edition]

## Chapter 6: Trigonometry

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4Exercise 6.5
Exercise 6.1 [Pages 227 - 228]

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 6 Trigonometry Exercise 6.1 [Pages 227 - 228]

Exercise 6.1 | Q 1 | Page 227

From the given figure, find all the trigonometric ratios of angle B

Exercise 6.1 | Q 2. (i) | Page 227

From the given figure, find the values of sin B

Exercise 6.1 | Q 2. (ii) | Page 227

From the given figure, find the values of sec B

Exercise 6.1 | Q 2. (iii) | Page 227

From the given figure, find the values of cot B

Exercise 6.1 | Q 2. (iv) | Page 227

From the given figure, find the values of cos C

Exercise 6.1 | Q 2. (v) | Page 227

From the given figure, find the values of tan C

Exercise 6.1 | Q 2. (vi) | Page 227

From the given figure, find the values of cosec C

Exercise 6.1 | Q 3 | Page 227

If 2 cos θ = sqrt(3), then find all the trigonometric ratios of angle θ

Exercise 6.1 | Q 4 | Page 227

If cos A = 3/5, then find the value of (sin"A" - cos"A")/(2tan"A")

Exercise 6.1 | Q 5 | Page 227

If cos A = (2x)/(1 + x^2), then find the values of sin A and tan A in terms of x

Exercise 6.1 | Q 6 | Page 227

If sin θ = "a"/sqrt("a"^2 + "b"^2), then show that b sin θ = a cos θ

Exercise 6.1 | Q 7 | Page 227

If 3 cot A = 2, then find the value of (4sin"A" - 3cos"A")/(2sin"A" + 3cos"A")

Exercise 6.1 | Q 8 | Page 227

If cos θ : sin θ = 1 : 2, then find the value of (8costheta - 2sintheta)/(4costheta + 2sintheta

Exercise 6.1 | Q 9 | Page 227

From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅

Exercise 6.1 | Q 10 | Page 228

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)

Exercise 6.2 [Page 232]

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 6 Trigonometry Exercise 6.2 [Page 232]

Exercise 6.2 | Q 1. (i) | Page 232

Verify the following equalities:

sin2 60° + cos2 60° = 1

Exercise 6.2 | Q 1. (ii) | Page 232

Verify the following equalities:

1 + tan2 30° = sec2 30°

Exercise 6.2 | Q 1. (iii) | Page 232

Verify the following equalities:

cos 90° = 1 – 2sin2 45° = 2cos2 45° – 1

Exercise 6.2 | Q 1. (iv) | Page 232

Verify the following equalities:

sin 30° cos 60° + cos 30° sin 60° = sin 90°

Exercise 6.2 | Q 2. (i) | Page 232

Find the value of the following:

(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)

Exercise 6.2 | Q 2. (ii) | Page 232

Find the value of the following:

(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)

Exercise 6.2 | Q 2. (iii) | Page 232

Find the value of the following:

sin2 30° – 2 cos3 60° + 3 tan4 45°

Exercise 6.2 | Q 3 | Page 232

Verify cos3A = 4cos3A – 3cosA, when A = 30°

Exercise 6.2 | Q 4 | Page 232

Find the value of 8 sin 2x, cos 4x, sin 6x, when x = 15°

Exercise 6.3 [Page 235]

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 6 Trigonometry Exercise 6.3 [Page 235]

Exercise 6.3 | Q 1. (i) | Page 235

Find the value of the following:

((cos 47^circ)/(sin 43^circ))^2 + ((sin 72^circ)/(cos 18^circ))^2 - 2cos^2 45^circ

Exercise 6.3 | Q 1. (ii) | Page 235

Find the value of the following:

(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ

Exercise 6.3 | Q 1. (iii) | Page 235

Find the value of the following:

tan 15° tan 30° tan 45° tan 60° tan 75°

Exercise 6.3 | Q 1. (iv) | Page 235

Find the value of the following:

cot theta/(tan(90^circ - theta)) + (cos(90^circ - theta) tantheta sec(90^circ - theta))/(sin(90^circ - theta)cot(90^circ - theta)"cosec"(90^circ - theta))

Exercise 6.4 [Page 239]

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 6 Trigonometry Exercise 6.4 [Page 239]

Exercise 6.4 | Q 1. (i) | Page 239

Find the value of the following:

sin 49°

Exercise 6.4 | Q 1. (ii) | Page 239

Find the value of the following:

cos 74° 39′

Exercise 6.4 | Q 1. (iii) | Page 239

Find the value of the following:

tan 54° 26′

Exercise 6.4 | Q 1. (iv) | Page 239

Find the value of the following:

sin 21° 21′

Exercise 6.4 | Q 1. (v) | Page 239

Find the value of the following:

cos 33° 53′

Exercise 6.4 | Q 1. (vi) | Page 239

Find the value of the following:

tan 70° 17′

Exercise 6.4 | Q 2. (i) | Page 239

Find the value of θ if sin θ = 0.9975

Exercise 6.4 | Q 2. (ii) | Page 239

Find the value of θ if cos θ = 0.6763

Exercise 6.4 | Q 2. (iii) | Page 239

Find the value of θ if tan θ = 0.0720

Exercise 6.4 | Q 2. (iv) | Page 239

Find the value of θ if cos θ = 0.0410

Exercise 6.4 | Q 2. (v) | Page 239

Find the value of θ if tan θ = 7.5958

Exercise 6.4 | Q 3. (i) | Page 239

Find the value of the following:

sin 65° 39′ + cos 24° 57’ + tan 10° 10′

Exercise 6.4 | Q 3. (ii) | Page 239

Find the value of the following:

tan 70° 58′ + cos 15° 26′ – sin 84° 59′

Exercise 6.4 | Q 4 | Page 239

Find the area of a right triangle whose hypotenuse is 10 cm and one of the acute angle is 24°24′

Exercise 6.4 | Q 5 | Page 239

Find the angle made by a ladder of length 5m with the ground, if one of its end is 4m away from the wall and the other end is on the wall

Exercise 6.4 | Q 6 | Page 239

In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is ∠P) measures 42° and the distance to the tree is 60 metres. Find the height of the tree

Exercise 6.5 [Pages 239 - 240]

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 6 Trigonometry Exercise 6.5 [Pages 239 - 240]

#### Multiple choice questions

Exercise 6.5 | Q 1 | Page 239

If sin 30° = x and cos 60° = y, then x2 + y2 is

• 1/2

• 0

• sin 90°

• cos 90°

Exercise 6.5 | Q 2 | Page 239

If tan θ = cot 37°, then the value of θ is

• 37°

• 53°

• 90°

Exercise 6.5 | Q 3 | Page 239

The value of tan 72° tan 18° is

• 0

• 1

• 18°

• 72°

Exercise 6.5 | Q 4 | Page 239

The value of (2tan30^circ)/(1 - tan^2 30^circ) is equal to

• cos 60°

• sin 60°

• tan 60°

• sin 30°

Exercise 6.5 | Q 5 | Page 240

If 2 sin 2θ = sqrt(3) then the value of θ is

• 90°

• 30°

• 45°

• 60°

Exercise 6.5 | Q 6 | Page 240

The value of 3 sin 70° sec 20° + 2 sin 49° sec 51° is

• 2

• 3

• 5

• 6

Exercise 6.5 | Q 7 | Page 240

The value of (1 - tan^2 45^circ)/(1 + tan^2 45^circ) is

• 2

• 1

• 0

• 1/2

Exercise 6.5 | Q 8 | Page 240

The value of cosec(70° + θ) – sec(20° − θ) + tan(65° + θ) – cot(25° − θ) is

• 0

• 1

• 2

• 3

Exercise 6.5 | Q 9 | Page 240

The value of tan 1° tan 2° tan 3°…. tan 89° is

• 0

• 1

• 2

• sqrt(3)/2

Exercise 6.5 | Q 10 | Page 240

Given that sin α = 1/2 and cos β = 1/2, then the value of α + β is

• 90°

• 30°

• 60°

## Chapter 6: Trigonometry

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4Exercise 6.5

## Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 6 - Trigonometry

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Concepts covered in Mathematics Class 9th Tamil Nadu State Board chapter 6 Trigonometry are Trigonometry, Trigonometric Ratios of Complementary Angles, Trigonometric Ratios and Its Reciprocal, Reciprocal Relation Between Trigonometric Ratios, Trigonometric Ratios of Some Special Angles, Method of Using Trigonometric Table.

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