Find arccos (sqrt2/2).
Can this be pi/4 and 7pi/4?
Could be :)
yes, those are the two values in the interval [0,2pi)
To find the arccos of a value, we need to determine the angle whose cosine is equal to that value. In this case, we are given the value sqrt(2)/2.
We know that the cosine of pi/4 is sqrt(2)/2. Therefore, the arccos(sqrt(2)/2) will be equal to pi/4.
However, it is important to note that the arccos function is defined to give us only one specific angle, which lies within the range [-π, π] or [0, 2π]. So, as per the standard convention, the range of arccos function is [0, π]. Therefore, the principal value of arccos(sqrt(2)/2) should be pi/4.
The alternate answer you mentioned, 7π/4, is not within the range of the standard arccos function. However, it is important to note that cosine has a periodic behavior with a period of 2π. This means that if arccos(sqrt(2)/2) equals pi/4, then adding any multiple of 2π to this angle will also be a correct answer. In this case, adding 2π to pi/4 gives us 9π/4, which is equivalent to 7π/4 since they are coterminal angles.
So, in conclusion, the arccos(sqrt(2)/2) is pi/4, and it is equivalent to 7π/4.