Final answer:
The tangent function represents the ratio of the opposite side to the adjacent side in a right triangle. tan(0) = 0. In interval notation, the values of x between 0 and 2π where tan(x) > 1 can be represented as (0, π/4) U (π/2, 3π/4) U (3π/2, 2π).
Step-by-step explanation:
The tangent function, denoted as tan(x), represents the ratio of the opposite side to the adjacent side in a right triangle. When x = 0, the opposite side is 0 and the adjacent side is 1, so tan(0) = 0/1 = 0.
Interval notation can be used to represent the values of x where tan(x) > 1. To find these values, we need to find the angles whose tangent is greater than 1. In the first quadrant, tan(x) is always positive. So, we need to find the angles in the first quadrant that have a tangent greater than 1.
One such angle is 45 degrees (π/4 radians). In interval notation, the values of x between 0 and 2π where tan(x) > 1 can be represented as (0, π/4) U (π/2, 3π/4) U (3π/2, 2π).