# Answer to Question #1764 in Trigonometry for Cas

Question #1764

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

Expert's answer

3 sin (θ) - 4 cos (θ) = 2

√(3

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'

√(3

^{2}+ 4^{2}) sin (θ - arctan(4/3)) = 2sin (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'**
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