Find the fundamental solutions to the following equation (between 0 ° and 360 ° ). − 12 cos ( θ ) − 11 tan ( θ ) = − 14 sec ( θ ) List your fundamental solutions in ascending order

Answer 1

-12cosθ-11tanθ=-14secθ

-12cosθ-11sinθ/cosθ=-14/cosθ

-12cosθ=(11sinθ-14)/cosθ

12(cosθ)^2=11sinθ-14

The best I can do is θ=42°; the difference is .0123925.........

Answer 2

-12 cos - 11 tan = -14 sec

-12 cos^2 - 11 sin = -14

12 cos^2 + 11 sin = 14

12 ( 1 - sin^2) + 11 sin = 14

12 - 12 sin^2 + 11 sin = 14

12 - 12 T^2 + 11 T = 14

0 = 14 - 12 + 12T^2 - 11T

0 = 12T^2 - 11T + 2

T = [11 +or- sqrt ( 121 - 96) ] / 24

T = [ 11 +or- sqrt( 25) ] / 24

T = [ 11 +or- 5 ] / 24

T = 16/24 = 2/3 or T = 6/24 = 1/4

sin x = 2/3

sine is positive in quadrants 1 and 2

x = arcsin(2/3) = 41.810314895778598065857916730578

or x = ‬138.18968510422140193414208326942

sin x = 1/4

x = arcsin(1/4) = 14.477512185929923878771034799127‬

or x = 165.52248781407007612122896520087