Solve the equation tan(x) = √3 for x in the interval [0, 2π].
Practice Questions
1 question
Q1
Solve the equation tan(x) = √3 for x in the interval [0, 2π].
π/3
2π/3
4π/3
5π/3
The solutions are x = π/3 and x = 4π/3 in the interval [0, 2π].
Questions & Step-by-step Solutions
1 item
Q
Q: Solve the equation tan(x) = √3 for x in the interval [0, 2π].
Solution: The solutions are x = π/3 and x = 4π/3 in the interval [0, 2π].
Steps: 6
Step 1: Understand the equation tan(x) = √3. This means we need to find angles x where the tangent of x equals √3.
Step 2: Recall that the tangent function is positive in the first and third quadrants.
Step 3: Find the reference angle where tan(x) = √3. This occurs at x = π/3 (or 60 degrees).
Step 4: Since tangent is positive in the third quadrant as well, we need to find the angle in that quadrant. This angle can be found by adding π to the reference angle: π/3 + π = 4π/3.
Step 5: Now we have two angles: x = π/3 and x = 4π/3.
Step 6: Check if both angles are within the interval [0, 2π]. Both π/3 and 4π/3 are within this interval.
