Find two values of 0, 0 ≤ 0 < 2π, that satisfy the following equation. Show your work.
tan 0 = √3/3
To find the values of 0 that satisfy the equation tan 0 = √3/3, we need to find the inverse tangent of √3/3.
We know that tan is positive in the first and third quadrants, so we need to find the angles whose tangent is √3/3 in those quadrants.
Using a calculator or reference table, we find that the inverse tangent of √3/3 is π/6 or 30 degrees.
Since tan is a periodic function with a period of π, we can add π to get another angle that satisfies the equation.
Therefore, the two values of 0 that satisfy tan 0 = √3/3 are π/6 (or 30 degrees) and π/6 + π (or 30 degrees + 180 degrees), which simplifies to 7π/6 (or 210 degrees).