Solve for x cos(x)=-12/13

Problem

cos(x)=−12/13

Solution

1. Identify the goal, which is to find the value of x that satisfies the equation.

2. Apply the inverse cosine function to both sides of the equation to isolate x

3. Determine the principal value by calculating arccos(−12/13) which falls in the interval [0,π]

4. Account for the periodicity of the cosine function, which repeats every 2*π radians.

5. Identify the second solution within one period using the symmetry property cos(x)=cos(−x) or 2*π−x

6. State the general solution by adding 2*π*n to both primary solutions, where n is any integer.

Final Answer

x=arccos(−12/13)+2*π*n,x=2*π−arccos(−12/13)+2*π*n

Want more problems? Check here!