Evaluate
$2\left(\frac{\tan 35^{\circ}}{\cot 55^{\circ}}\right)+\left(\frac{\cot 55^{\circ}}{\tan 35^{\circ}}\right)-3\left(\frac{\sec 40^{\circ}}{\cos e c 50^{\circ}}\right)$
Answer
$2\left(\frac{\tan 35^{\circ}}{\cot 55^{\circ}}\right)+\left(\frac{\cot 55^{\circ}}{\tan 35^{\circ}}\right)-3\left(\frac{\sec 40^{\circ}}{\cos e c 50^{\circ}}\right) $
$=2\left(\frac{\tan \left(90^{\circ}-55^{\circ}\right)}{\cot 55^{\circ}}\right)+\left(\frac{\cot \left(90^{\circ}-35^{\circ}\right)}{\tan 35^{\circ}}\right)-3\left(\frac{\sec \left(90^{\circ}-50^{\circ}\right)}{\cos e c 50^{\circ}}\right)$
$ =2\left(\frac{\cot 55^{\circ}}{\cot 55^{\circ}}\right)+\left(\frac{\tan 35^{\circ}}{\tan 35^{\circ}}\right)-3\left(\frac{\cos e c 50^{\circ}}{\cos e c 50^{\circ}}\right) $
$ =2(1)^2+1^2+-3 $
$=2+1-3$
$=0$
Use tables to find the acute angle θ, if the value of tan θ is0.7391
Answer
From the tables, it is clear that tan 36° 24’ = 0.7373 tan θ − tan 36° 24’ = 0.7391 − 0.7373 = 0.0018 From the tables, diff of 4’ = 0.0018 Hence, θ = 36° 24’ + 4’ = 36° 28’
Use tables to find the acute angle θ, if the value of tan θ is0.4741
Answer
From the tables, it is clear that tan 25° 18’ = 0.4727 tan θ − tan 25° 18’ = 0.4741 − 0.4727 = 0.0014 From the tables, diff of 4’ = 0.0014 Hence, θ = 25° 18’ + 4’ = 25° 22’
Use tables to find the acute angle θ, if the value of cos θ is0.6885
Answer
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, θ = 46° 30’ − 1’ = 46° 29’
Use tables to find the acute angle θ, if the value of cos θ is0.9574
Answer
From the tables, it is clear that cos 16° 48’ = 0.9573 cos θ − cos 16° 48’ = 0.9574 − 0.9573 = 0.0001 From the tables, diff of 1’ = 0.0001 Hence, θ = 16° 48’ − 1’ = 16° 47’
Use tables to find the acute angle θ, if the value of sin θ is0.6525
Answer
From the tables, it is clear that sin 40° 42' = 0.6521 sin θ − sin 40° 42' = 0.6525 −; 0.6521 = 0.0004 From the tables, diff of 2' = 0.0004 Hence, θ = 40° 42' + 2' = 40° 44