Find the value of: sin 65' 39 +cos 24'57'+tan 10'10'.
Answers
Answer:
Example 1 :
Find the value of the following:
(i) sin 49°
Solution :
sin 49° = 0.7547
(ii) cos 74° 39'
Solution :
cos 74° 39'
= cos 74° 36' + 3'
= 0.2656 - 0.008
= 0.2648
(iii) tan 54° 26'
Solution :
tan 54° 26' = tan 54° 24' + 2''
= 1.3968 + 0.0017
= 1.3985
(iv) sin 21° 21'
Solution :
sin 21° 21' = sin 21° 18' + 3''
= 0.3633 + 0.0008
= 0.3641
(v) cos 33° 53'
Solution :
cos 33° 53' = cos 33° 48' - 5''
= 0.8310 - 0.0008
= 0.8302
(vi) tan 70° 17'
Solution :
tan 70° 17' = tan 70° 12' + 5''
= 2.2776 + 0.0131
= 2.2907
Example 2 :
Find the value of θ if
(i) sin θ = 0.9975 (ii) cos θ = 0.6763 (iii) tan θ = 0.0720
Solution :
(i) sin θ = 0.9975
= sin 85° 57'
(ii) cos θ = 0.6763
= sin 47° 27'
(iii) cos θ = 0.6763
= sin 4° 7'
(iv) cos θ = 0.0410
= sin 87° 39'
(v) cos θ = 7.5958
= cos 82° 30'
Find the value of the following:
(i) sin 65° 39' + cos 24° 57' + tan 10° 10'
Solution :
sin 65° 39' = sin 65° 36' + 3''
= 0.9107 + 0.0004
= 0.9111
cos 24° 57' = 0.9070 - 0.0004
= 0.9066
tan 10° 10' = 0.1781 + 0.0012
= 0.1793
sin 65°39'+cos 24°57'+tan 10°10'
= 0.9111 + 0.9066 + 0.1793
= 1.997
(ii) tan 70° 58' + cos 15° 26' - sin 84° 59'
Solution :
tan 70° 58' = tan 70° 54' + 4''
= 2.8878 + 0.0104
= 2.8982
cos 15° 26' = cos 15° 24' - 2''
= 0.9641 - 0.0004
= 0.9637
sin 84° 59' = sin 84° 54' + 5''
= 0.9960 + 0.0002
= 0.9962
tan 70° 58' + cos 15° 26' - sin 84° 59'
= 2.8982 + 0.9637 - 0.9962
= 2.8657