Solve for x 2sin(x)+5=6

Problem

2*sin(x)+5=6

Solution

1. Isolate the term containing the sine function by subtracting 5 from both sides of the equation.

2*sin(x)=1

2. Divide both sides by 2 to solve for the sine of x

sin(x)=1/2

3. Determine the reference angle by finding the inverse sine of 1/2

x=arcsin(1/2)

4. Identify the general solutions within one full rotation, 0≤x<2*π noting that sine is positive in the first and second quadrants.

x=π/6

x=π−π/6=(5*π)/6

5. Generalize the solution to include all possible values by adding multiples of the period 2*π where n is any integer.

x=π/6+2*n*π

x=(5*π)/6+2*n*π

Final Answer

x=π/6+2*n*π,(5*π)/6+2*n*π

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