Solve for x 2sin(3x)+1=0

Problem

2*sin(3*x)+1=0

Solution

1. Isolate the sine term by subtracting 1 from both sides and then dividing by 2.

2*sin(3*x)=−1

sin(3*x)=−1/2

2. Identify the reference angle for which the sine value is 1/2 which is π/6 Since the sine value is negative, the angle 3*x must be in the third or fourth quadrant.

3*x=(7*π)/6+2*π*n

3*x=(11*π)/6+2*π*n

3. Solve for x by dividing all terms in both general solutions by 3.

x=(7*π)/18+(2*π*n)/3

x=(11*π)/18+(2*π*n)/3

Final Answer

x=(7*π)/18+(2*π*n)/3,(11*π)/18+(2*π*n)/3

Want more problems? Check here!