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Sarah, Tutor / Ex-Teacher

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PLANE TRIGONOMETRY PART 3

Resolved Question:

1)FIND THE SINE, CONSINE, TANGENT, AND COTANGENT OF: a)122 DEGREES b)315 DEGREES 12' c)275 DEGREES 13' 37" d)193 DEGREES 41' 51"
2)USING EXACT VALUES, FIND THE NUMERICAL VALUE OF: a)sin 30 DEGREES cos 240 DEGREES +sin 210 DEGREES sin 300 DEGREES b)tan 225 DEGREES + tan (-45 DEGREES)
3)EXPRESS EACH OF THE FOLLOWING AS THE SAME FUNCTION OF A POSITIVE ACUTE ANGLE: a)cos 112 DEGREES 33' b)tan 310 DEGREES c)cot 138 DEGREES 15' 10" d)sin (-140 DEGREES)4)EXPRESS EACH AS A FUNCTION OF 0:a)sin (270 DEGREES + 0) b)cos (pi + 0) c)tan (810 DEGREES + 0) d)sin (0-180 DEGREES)5)FIND THE VALUE OF: a)log sin 62 DEGREES 22' 33" b)log cot 28 DEGREES 13' 17" c)log cos 125 DEGREES 15' 23" d)log tan 78 DEGREES 45' 50" 6)FIND THE ACUTE ANGLE A, TO THE NEAREST SECOND, WHEN: a)log cos A=9.12575 b)log sin A=9.91655 c)log cot A=0.11975 d)log tan A=0.063237)SIMPLIFY: sin(90 DEGREES+x)sin (180 DEGREES+x)cos(90 DEGREES+x)cos(180 DEGREES-x) 8)SOLVE THE RIGHT TRIANGLE BY LOGARITHMS:A=28 DEGREES 30', b=18.3

I am not entirely sure what this is asking. The problems as stated already are functions of 0 technically, and you could write each answer in various different ways incorporating 0....

c)log cos 125 DEGREES 15' 23" = No answer, because cos 125 is a negative number and you can't take log of a negative number.

d)log tan 78 DEGREES 45' 50" = 0.702

6)FIND THE ACUTE ANGLE A, TO THE NEAREST SECOND, WHEN:

There are no solutions to (a) or (b) as I understand the problem - as you can see in the work below, finding A is out of the domain range because cos of any angle could never equal 10^{9.12575} - a number much much bigger than 1. Am I misreading the problem? I believe this is log_{10}(cosA) = 9.12575. Is this correct??? Please email me back and we will see if we can figure this out.

i also need more answers,
solve the following oblique triangles 9)a = 31,b = 15, c = 17
10)a = 23.47, b = 115 degrees 30', c= 20 degrees 29' 11)a = 134.2,b = 84.54, B = 52 degrees 9' 11" 12)a = 627.7, b = 412.2, A = 66 degrees 47'

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