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

Problem

cos(x)=√(,2)/2

Solution

1. Identify the values on the unit circle where the x-coordinate is equal to √(,2)/2

2. Determine the reference angle in the first quadrant, which is x=π/4 or 45

3. Find the second solution in the fourth quadrant where the cosine function is also positive, which is x=2*π−π/4=(7*π)/4 or 315

4. Generalize the solution to include all possible rotations by adding multiples of 2*π (or 360, where n is any integer.

Final Answer

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

Want more problems? Check here!