Answer to Question #1764 in Trigonometry for Cas

Question

Solve this trigonometric equation.give all positive values of the angle between 0deg and 360deg that will satisfy.
Give any approximate value to the nearest minute only.

3 sin theta - 4 cos theta =2

Answer 1

3 sin (θ) - 4 cos (θ) = 2
√(3² + 4²) sin (θ - arctan(4/3)) = 2
sin (θ - arctan(4/3)) = 2/5
θ = arctan(2/5) + arctan(4/3) + π n, n = 0,1,..
θ = 21.8 + 53.13 + π n = 74.93 + π n [ n = 0,1,.. ]= 74° 56', 254° 56'
Answer: 74° 56', 254° 56'