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

Problem

2*sin(x)+3=2

Solution

1. Isolate the sine term by subtracting 3 from both sides of the equation.

2*sin(x)=2−3

2*sin(x)=−1

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

sin(x)=−1/2

3. Identify the reference angle by finding the value where sin(θ)=1/2

θ=π/6

4. Determine the quadrants where the sine function is negative, which are Quadrant III and Quadrant IV.

x=π+π/6=(7*π)/6

x=2*π−π/6=(11*π)/6

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

x=(7*π)/6+2*n*π

x=(11*π)/6+2*n*π

Final Answer

x=(7*π)/6+2*n*π,(11*π)/6+2*n*π

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