Solve for x sin(x)=0.5

Problem

sin(x)=0.5

Solution

1. Identify the reference angle by finding the inverse sine of the absolute value of the constant.

sin(x)=1/2

x=arcsin(1/2)

x=π/6

2. Determine the quadrants where the sine function is positive. Sine is positive in Quadrant I and Quadrant II.

3. Calculate the general solution for Quadrant I using the reference angle and the period of sine, which is 2*π

x=π/6+2*n*π

4. Calculate the general solution for Quadrant II by subtracting the reference angle from π

x=π−π/6+2*n*π

x=(5*π)/6+2*n*π

5. Define the variable n as any integer to represent all possible solutions.

n∈ℤ

Final Answer

sin(x)=0.5⇒x=π/6+2*n*π,(5*π)/6+2*n*π

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