Solve for x cos(x)=4/5

Problem

cos(x)=4/5

Solution

1. Identify the goal, which is to find the value of x that satisfies the equation. Since the cosine function is periodic, there are infinitely many solutions unless a specific interval is provided.

2. Apply the inverse cosine function to both sides of the equation to isolate x This gives the principal value, often called the arccosine.

x=arccos(4/5)

3. Determine the general solution for x Because cos(x) is an even function, if x is a solution, then −x is also a solution. Furthermore, the cosine function has a period of 2*π

x=±arccos(4/5)+2*π*n

4. Define the integer constant n where n represents any integer (n∈ℤ.

Final Answer

cos(x)=4/5⇒x=±arccos(4/5)+2*π*n

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