Solve for x cos(x)=( square root of 3)/2

Problem

cos(x)=√(,3)/2

Solution

1. Identify the reference angle in the first quadrant where the cosine value is √(,3)/2

cos(π/6)=√(,3)/2

2. Determine the general solution for the cosine function, which is periodic with a period of 2*π and symmetric across the x-axis.

x=±π/6+2*k*π

3. Define the variable k as any integer to represent all possible solutions.

k∈ℤ

Final Answer

cos(x)=√(,3)/2⇒x=π/6+2*k*π,−π/6+2*k*π

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