π/4 (√2/2, √2/2)
theta = pi/4
The point (sqrt(2)/2, sqrt(2)/2) lies on the unit circle since the radius of the unit circle is 1, and sqrt(2)/2 squared plus sqrt(2)/2 squared is equal to 1.
To find the angle at which this point is located on the unit circle, we use the inverse tangent function, which gives us:
tan(theta) = y/x = sqrt(2)/2 / sqrt(2)/2 = 1
Therefore, theta = tan^(-1)(1). Since tan(pi/4) = 1, it follows that theta = pi/4.
In summary, pi/4 (sqrt(2)/2, sqrt(2)/2) represents a point on the unit circle located at an angle of pi/4 radians or 45 degrees above the positive x-axis.
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