Find all solutions to the equation.
$\cos x=1$

• A. $x=0$
• B. $x=2\pi n$
• C. $x=\pi+2\pi n$
• D. $x=\frac{\pi}{2}+2\pi n,x=\frac{3\pi}{2}+2\pi n$

Answer: (B)

Verified step by step guidance

1. Start by understanding the equation cos(x) = 1. The cosine function equals 1 at specific points on the unit circle.
2. Recall that the cosine function has a period of 2π, meaning it repeats its values every 2π radians.
3. The primary angle where cos(x) = 1 is at x = 0. Since the cosine function is periodic, the general solution for cos(x) = 1 is x = 2πn, where n is an integer.
4. Consider other angles where the cosine function might equal 1. However, for cosine, the only angle in the interval [0, 2π) where cos(x) = 1 is x = 0.
5. Thus, the complete set of solutions for the equation cos(x) = 1 is given by x = 2πn, where n is any integer, representing the periodic nature of the cosine function.