Solve for x cos(x)=5/13

Problem

cos(x)=5/13

Solution

1. Identify the equation as a basic trigonometric equation where the cosine of an angle x is a positive constant.

2. Apply the inverse cosine function to both sides of the equation to find the principal value, often called the arccosine.

x=arccos(5/13)

3. Account for the periodicity and symmetry of the cosine function. Since cos(x)=cos(−x) and the function repeats every 2*π radians, the general solution includes both positive and negative results plus multiples of 2*π

x=±arccos(5/13)+2*π*n

4. Define the integer variable n which represents any integer (n=0,±1,±2,….

Final Answer

cos(x)=5/13⇒x=±arccos(5/13)+2*π*n

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