Final answer:
The values of φ where tan(φ) > 1 between 0 and 2π are in the intervals (π/4, π/2) and (5π/4, 3π/2), which correspond to the first and third quadrants where the tangent function is positive and greater than 1.
Step-by-step explanation:
To solve the mathematical problem completely, we need to determine the intervals where tan(φ) is greater than 1 between 0 and 2π.
The tangent function, given by tan(φ), is the ratio of the sine function to the cosine function. It is positive where the angles are in the first and third quadrants.
In the interval between 0 and 2π, tan(φ) > 1 occurs in the first quadrant from π/4 to π/2 and in the third quadrant from 5π/4 to 3π/2.
Therefore, using interval notation, these intervals can be represented as: