If cosx=sqrt{3}/2 and −pi/2<=x<=0 then the exact value of x, in radians
To find the exact value of x, we can use the inverse cosine function (arccos) to get the angle whose cosine is sqrt(3)/2.
The inverse cosine function is defined as cos^(-1)(cos(x)) = x.
In this case, we have cos(x) = sqrt(3)/2. We need to find the value of x in the given range −π/2 ≤ x ≤ 0.
Since the cosine function is positive in the given range, we can use the positive value of arccos(sqrt(3)/2) to find the exact value of x.
arccos(sqrt(3)/2) is the angle whose cosine is sqrt(3)/2.
It is a special angle which occurs in the unit circle when the reference angle is π/6 (30 degrees). In radians, this angle is π/6.
Therefore, the exact value of x is π/6 radians.
To find the exact value of x in radians, we need to determine the angle in the given range that has a cosine value of sqrt(3)/2.
In the range -pi/2 <= x <= 0, we already know that cos(x) = sqrt(3)/2.
The angle whose cosine is sqrt(3)/2 is pi/6.
Since the given range is -pi/2 <= x <= 0, the exact value of x in radians is pi/6.