Selina solutions concise maths class 9 icse Solutions for Chapter 22 chapter 22 trigonometrical ratios

Exercises in Chapter 22 chapter 22 trigonometrical ratios Grade 9

Exercise 22(A)

Exercise 22(B)

Questions in Exercise 22(A)

From the following figure, find the values of :

(i) sin A

(ii) cos A

(iii) cot A

(iv) sec C

(v) cosec C

(vi) tan C

Form the following figure, find the values of :

(i) cos B

(ii) tan C

(iii) sin2B + cos2B

(iv) sin B. cos C + cos B. sin C

From the following figure, find the values of :

(i) cos A

(ii) cosec A

(iii) tan2A - sec2A

(iv) sin C

(v) sec C

(vi) cot2 C - 𝟏/ 𝑺𝒊𝒏𝟐C

From the following figure, find the values of :

(i) sin B

(ii) tan C

(iii) sec2 B - tan2B

(iv) sin2C + cos2C

Given: sin A = 3/5 , find :

(i) tan A

(ii) cos A

From the following figure, find the values of :

(i) sin A

(ii) sec A

(iii) cos2 A + sin2A

Given: cos A = 5 / 13

Evaluate:

Given: sec A = 29/21, evaluate : sin A – (1/tan A)

Given: tan A = 4/3, find:

Given: 4 cot A = 3 find;

(i) sin A

(ii) sec A

(iii) cosec2 A - cot2A.

Given: cos A = 0.6; find all other trigonometrical ratios for angle A.

In a right-angled triangle, it is given that A is an acute angle and tan A = 5/12. find the value of :

(i) cos A

(ii) sin A

Given: sin 𝜽 = p/q

Find cos 𝜽 + sin 𝜽 in terms of p and q.

If cos A = ½ and sin B = 1/√𝟐, find the value of :

Are angles A and B from the same triangle? Explain.

If 5 cot 𝜽= 12, find the value of Cosec 𝜽 + sec 𝜽

If tan x = 𝟏 (𝟏)/ (𝟑) , find the value of : 4 sin2x - 3 cos2x + 2

If cosec 𝜽 = √𝟓, find the value of:

(i) 2 - sin2𝜽 -cos2𝜽

(ii)

If sec A = √𝟐, find the value of :

If cot 𝜽= 1; find the value of: 5 tan2𝜽+ 2 sin2 𝜽- 3

In the following figure:

AD BC, AC = 26 CD = 10, BC = 42,

∠ DAC = x and ∠ B = y.

Concise Selina Solutions for Class 9 Maths Chapter 22-

Trigonometrical Ratios

Find the value of :

(i) cot x

Questions in Exercise 22(B)

From the following figure, find:

(i) y

(ii) sin x °

(iii) (sec x° -tan x° ) (sec x° +tan x° )

Question 1 Image - Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 22- Trigonometrical Ratios

Use the given figure to find:

(i) sin x °

(ii) cos y°

(iii) 3 tan x° -2 sin y° +4 cos y° .

Question 2 Image - Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 22- Trigonometrical Ratios

In the diagram, given below, triangle ABC is right-angled at B and BD is perpendicular to AC. Find:

(i) cos ∠DBC

(ii) cot ∠DBA

In the given figure, triangle ABC is right-angled at B. D is the foot of the perpendicular from B to AC. Given that BC = 3 cm and AB = 4 cm. find:

(i) tan DBC

(ii) sin DBA

In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC.

In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:

(i) sin B

(ii) tan C

(iii) sin2 B + cos2B

(iv) tan C - cot B

In triangle ∠ ABC; ∠ ABC = 90 ° , CAB = x° , tan x° = ¾ and BC = 15 cm. Find the measures of AB and AC.

Using the measurements given in the following figure:

(i) Find the value of sinΦ and tanθ.

(ii) Write an expression for AD in terms of θ

In the given figure;

BC = 15 cm and sin B = 4/5

(i) Calculate the measure of AB and AC.

(ii) Now, if tan ADC = 1; calculate the measures of CD and AD.

Also, show that: tan2B – 1/ cos2B = -1

If sin A + cosec A = 2;

Find the value of sin2 A + cosec2 A.

If tan A + cot A = 5;

Find the value of tan2 A + cot2 A.

Given: 4 sin 𝜽 = 3 cos𝜽; find the value of:

(i) sin 𝜽

(ii) cos 𝜽

(iii) cot2 𝜽 - cosec2 𝜽.

(iv) 4 cos2 𝜽 - 3 sin2 𝜽 + 2

Given : 17 cos 𝜽 = 15;

Find the value of tan 𝜽 + 2sec 𝜽.

Given : 5 cos A - 12 sin A = 0; evaluate :

In the given figure; C = 90o and D is the mid-point of AC. Find

If 3 cos A = 4 sin A, find the value of :

(i) cos A

(ii) 3 - cot2 A + cosec2A

In triangle ABC, B = 90 ° and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.

In rhombus ABCD, diagonals AC and BD intersect each other at point O.

If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the side and the diagonals of the rhombus.

In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:

(i) cos B

(ii) sin C

(iii) tan2 B - sec2 B + 2

In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C = 1. Find the length of AB, AD, AC, and DC.

Given q tan A = p, find the value of :

If sin A = cos A, find the value of 2 tan2A - 2 sec2 A + 5.

In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the the perimeter of the rectangle ABCD.

If sin A = √ 3/2 and cos B =√ 3/2, find the value of :

Use the information given in the following figure to evaluate:

10/sin x + 6/sin y - 6cot y

If sec A = √𝟐,

find:

If 5 cos 𝜽 = 3,

cosec 𝜽 - cot 𝜽 / cosec 𝜽 + cot 𝜽

find:

If cosec A + sin A = 5(𝟏)/ (𝟓) , find the value of cosec2A + sin2A

If 5 cos 𝜽 = 6 sin 𝜽 ; evaluate:

(i) tan 𝜽

(ii) 12 sin 𝜽 - 3 cos 𝜽/ 12 sin 𝜽 + 3 cos 𝜽

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Chapters in this book

Chapter 1- Rational and Irrational Numbers

Chapter 2- Compound Interest [Without Using Formula

Chapter 3- Compound Interest [Using Formula

Chapter 4- Expansions

Chapter 5- Factorisation

Chapter 6- Simultaneous Equations

Chapter 7- Indices [exponents]

Chapter 8- Logarithms

Chapter 9- Triangles [Congruency in Triangles]

Chapter 10- Isosceles Triangle

Chapter 11- Inequalities

Chapter 12- Mid-Point and Its Converse

Chapter 13- Pythagoras Theorem

Chapter 14- Rectilinear Figures

Chapter 15- Construction of Polygons

Chapter 16- Area Theorems

Chapter 17- Circles

Chapter 18- Statistics

Chapter 19- Mean and Median

Chapter 20- Area and Perimeter of Plane Figures

Chapter 21- Solids

Chapter 22- Trigonometrical Ratios

Chapter 23- Trigonometrical Ratios of Standard Angles

Chapter 24- Solution Of Right Triangles

Chapter 25- Complementary angles

Chapter 26- Co-ordinate Geometry

Chapter 27- Graphical Solution

Chapter 28- Distance Formula