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

Problem

cos(x)=√(,2)/2

Solution

1. Identify the reference angle on the unit circle where the cosine value is √(,2)/2

2. Determine the primary solution in the first quadrant, which is x=π/4 (or 45.

3. Determine the second solution in the fourth quadrant, where cosine is also positive, using the symmetry 2*π−θ

4. Calculate the second value: 2*π−π/4=(7*π)/4

5. Generalize the solutions to account for the periodicity of the cosine function by adding 2*k*π where k is any integer.

Final Answer

cos(x)=√(,2)/2⇒x=π/4+2*k*π,(7*π)/4+2*k*π

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