Final answer:
To find the value of tangent (arc cosine (negative sqrt(2)/2)), we first find the angle, then use the tangent function.
Step-by-step explanation:
To find the value of tangent (arc cosine (negative sqrt(2)/2)), we need to first find the angle whose cosine is negative sqrt(2)/2.
Since the cosine of an angle is equal to the x-coordinate of a point on the unit circle, we can determine that the angle is 135 degrees or 3π/4 radians.
Now, we can use the tangent function to find the value by dividing the y-coordinate of the point on the unit circle by the x-coordinate. In this case, the y-coordinate is -1/sqrt(3), so the tangent of the angle is -1/sqrt(3).