Find all the solutions in the interval [0,2pi] to cosx=square root 2/2
We can solve this equation by taking the inverse cosine (also known as arccos) of both sides. Using the identity arccos(cos(x)) = x, we have:
x = arccos(sqrt(2)/2)
Now, using the unit circle, we can see that sqrt(2)/2 corresponds to the angle pi/4 or 45 degrees. Since we are looking for solutions in the interval [0,2pi], we need to determine the angles that are pi/4 radians apart.
The other angle that is pi/4 radians apart from pi/4 is 5*pi/4.
Therefore, the solutions in the interval [0,2pi] are x = pi/4 and x = 5*pi/4.