ML Aggarwal Solution Class 10 Chapter 19 Trigonometric Tables Test

 Test

Question 1

Using trigonometrical tables, find the values of :

(i) sin 48° 52′

(ii) cos 37° 34′

(iii) tan 18° 21′.

Sol :

Using tables, we find that

(i) sin 48° 52′ = .7524 + .0008 = .7532

(ii) cos 37° 34′ = .7934 – .0007 = .7927

(iii) tan 18° 21′ = .3307 + .0010 = .3317.


Question 2

Use tables to find the acute angle θ, given that

(i) sin θ = 0.5766

(ii) cos θ = 0.2495

(iii) tan θ = 2.4523.

Sol :

Using table, we find that

(i) sin θ = 0.5766 = 0.5764 + 0.0002

= sin (35° 12’+ 1′)

= sin 35° 13′

θ = 35° 13′

(ii) cos θ = 0.2495 = 0.2487 + 0.0008

= cos (75° 36′ – 3′)

= cos 75° 33′

θ = 75° 33′

(iii) tan θ = 2.4523 = 2.4504 + 0.0019

= tan (67° 48′ + 1′)

= tan 67° 49′


Question 3

If θ is acute and cos θ = 0.53, find the value of tan θ.

Sol :

From the table, we find that

cos θ = 0.53 = .5299 + .0001 = cos 58°

θ = 58°

and tan 58° = 1.6003


Question 4

Find the value of: sin 22° 11′ + cos 57° 20′ – 2 tan 9° 9′.

Sol :

Using the tables, we find that

sin 22° 11′ = 0.3762 + 0.0014 = 0.3776

cos 57° 20′ = 0.5402 – 0.0005 = 0.5397

tan 9° 9′ = 0.1602 + 0.0009 = 0.1611

∴ sin 22° 11′ + cos 57° 20′ – 2 tan 9° 9′

= 0.3376 + 0.5397 – 0.1611 × 2

= 0.3776 + 0.5397 – 0.3222

= 0.9173 – 0.3222

= .5951.


Question 5

If θ is acute and sin θ = 0.7547, find the value of: (i) θ (ii) cos θ (iii) 2 cos θ – 3 tan θ.

Sol :

Using the tables, we find that

(i) sin θ = 0.7547 = sin 49°

θ = 49°.

(ii) cos θ = cos 49° = 0.6561.

(iii) tan θ = tan 49° = 1.1504

2 cos θ – 3 tan θ

= 2 × θ.6561 – 3 × 1.1504

= 1.3122 – 3.4512

= – 2.1390

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