Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(D)

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(D)

Question 1

Use tables to find sine of:

(i) 21°

(ii) 34° 42'

(iii) 47° 32'

(iv) 62° 57'

(v) 10° 20' + 20° 45'

Solution 1

(i) sin 21^o = 0.3584

(ii) sin 34^o 42'= 0.5693

(iii) sin 47^o 32'= sin (47^o 30' + 2') =0.7373 + 0.0004 = 0.7377

(iv) sin 62^o 57' = sin (62^o 54' + 3') = 0.8902 + 0.0004 = 0.8906

(v) sin (10^o 20' + 20^o 45') = sin 30^o65' = sin 31^o5' = 0.5150 + 0.0012 = 0.5162

Question 2

Use tables to find cosine of:

(i) 2° 4’

(ii) 8° 12’

(iii) 26° 32’

(iv) 65° 41’

(v) 9° 23’ + 15° 54’

Solution 2

(i) cos 2° 4’ = 0.9994 - 0.0001 = 0.9993

(ii) cos 8° 12’ = cos 0.9898

(iii) cos 26° 32’ = cos (26° 30’ + 2’) = 0.8949 - 0.0003 = 0.8946

(iv) cos 65° 41’ = cos (65° 36’ + 5’) = 0.4131 -0.0013 = 0.4118

(v) cos (9° 23’ + 15° 54’) = cos 24° 77’ = cos 25° 17’ = cos (25° 12’ + 5’) = 0.9048 - 0.0006 = 0.9042

Question 3

Use trigonometrical tables to find tangent of:

(i) 37°

(ii) 42° 18'

(iii) 17° 27'

Solution 3

(i) tan 37^o = 0.7536

(ii) tan 42^o 18' = 0.9099

(iii) tan 17^o  27' = tan (17^o 24' + 3') = 0.3134 + 0.0010 = 0.3144

Question 4

Use tables to find the acute angle , if the value of sin  is:

(i) 0.4848

(ii) 0.3827

(iii) 0.6525

Solution 4

(i) From the tables, it is clear that sin 29^o = 0.4848

Hence, = 29^o

(ii) From the tables, it is clear that sin 22^o 30' = 0.3827

Hence,  = 22^o 30'

(iii) From the tables, it is clear that sin 40^o 42' = 0.6521

sin  - sin 40^o 42' = 0.6525 -; 0.6521 = 0.0004

From the tables, diff of 2' = 0.0004

Hence,  = 40^o  42' + 2' = 40^o 44'

Question 5

Use tables to find the acute angle , if the value of cos  is:

(i) 0.9848

(ii) 0.9574

(iii) 0.6885

Solution 5

(i) From the tables, it is clear that cos 10° = 0.9848

Hence,  = 10°

(ii) From the tables, it is clear that cos 16° 48’ = 0.9573

cos  - cos 16° 48’ = 0.9574 - 0.9573 = 0.0001

From the tables, diff of 1’ = 0.0001

Hence,  = 16° 48’ - 1’ = 16° 47’

(iii) From the tables, it is clear that cos 46° 30’ = 0.6884

cos q - cos 46° 30’ = 0.6885 - 0.6884 = 0.0001

From the tables, diff of 1’ = 0.0002

Hence,  = 46° 30’ - 1’ = 46° 29’

Question 6

Use tables to find the acute angle , if the value of tan q is:

(i) 0.2419

(ii) 0.4741

(iii) 0.7391

Solution 6

(i) From the tables, it is clear that tan 13° 36’ = 0.2419

Hence,  = 13° 36’

(ii) From the tables, it is clear that tan 25° 18’ = 0.4727

tan  - tan 25° 18’ = 0.4741 - 0.4727 = 0.0014

From the tables, diff of 4’ = 0.0014

Hence,  = 25° 18’ + 4’ = 25° 22’

(iii) From the tables, it is clear that tan 36° 24’ = 0.7373

tan  - tan 36° 24’ = 0.7391 - 0.7373 = 0.0018

From the tables, diff of 4’ = 0.0018

Hence,  = 36° 24’ + 4’ = 36° 28’