Find two values of 0, 0 ≤ 0 < 2π, that satisfy the following equation. Show your work.
tan0 = √3/3
To find the values of θ that satisfy the equation tanθ = √3/3, we need to find the inverse tangent of √3/3.
The inverse tangent is denoted as tan^(-1) or arctan, and it provides the angle whose tangent is a given value.
Using a calculator or a table of trigonometric values, we can find that arctan(√3/3) ≈ 0.615.
Since the range of the inverse tangent function is (-π/2, π/2), we know that θ is between -π/2 and π/2.
To find the second value of θ, we can add π to the first value:
θ = 0.615 + π
Thus, the two values of θ that satisfy the equation tanθ = √3/3 are approximately 0.615 and 3.757.