Solve for x cos(x)=1/( square root of 2)

Problem

cos(x)=1/√(,2)

Solution

1. Rationalize the denominator of the constant on the right side of the equation to identify the standard trigonometric value.

1/√(,2)=√(,2)/2

2. Identify the reference angle in the first quadrant where the cosine function equals √(,2)/2

x=π/4

3. Determine the second location on the unit circle where the cosine is positive, which occurs in the fourth quadrant.

x=2*π−π/4=(7*π)/4

4. Generalize the solution to include all possible rotations by adding multiples of the period 2*π where n is any integer.

x=π/4+2*n*π

x=(7*π)/4+2*n*π

Final Answer

cos(x)=1/√(,2)⇒x=π/4+2*n*π,(7*π)/4+2*n*π

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