Solve for x 4sin(x)-1=2sin(x)

Problem

4*sin(x)−1=2*sin(x)

Solution

1. Isolate the trigonometric terms by subtracting 2*sin(x) from both sides of the equation.

4*sin(x)−2*sin(x)−1=0

2*sin(x)−1=0

2. Move the constant term to the other side by adding 1 to both sides.

2*sin(x)=1

3. Divide both sides by 2 to solve for sin(x)

sin(x)=1/2

4. Identify the angles x that satisfy the equation within the standard interval [0,2*π) The sine function is positive in the first and second quadrants.

x=π/6

x=π−π/6=(5*π)/6

5. Generalize the solution by adding multiples of the period 2*π to account for all possible solutions.

x=π/6+2*k*π

x=(5*π)/6+2*k*π

Final Answer

x=π/6+2*k*π,(5*π)/6+2*k*π

Want more problems? Check here!