Solving Trigonometric Equations

Question

Solve 4 sin x + 5 = 4 + sin x to the nearest thousandth.

a. In the domain 0° ≤ x ≤ 360°

b. In the domain of the real numbers, as a general solution.

Answer 1

4 sin x + 5 = 4 + sin x =

3sinx = -1

sinx = -1/3

x = arcsin (-1/3) = about -19.471

From 0 <=x <=360 it's in the 3rd and 4th quadrants, 19.471 degrees away from 180 and 360.

180+19.471 = 199.471

360-19.471 = 340.529

General solution is 199.471 + 360n and 340.529 + 360n where n is 0...infinity.