Question

Find all solutions of the equation in the interval [0, 21). tan 0+√3=0 Write your answer in radians in terms of π. If there is more than one solution, separate them with comma

Answer 1

The solutions to the equation tan θ + √3 = 0 in the interval [0, 2π) are 2π/3 and 5π/3 radians.

Step-by-step explanation:

To find all solutions of the equation tan θ + √3 = 0 in the interval [0, 2π), we can rewrite the equation as tan θ = -√3. This corresponds to an angle where the tangent is negative and has the same absolute value as the tangent of π/3, which is √3. The two angles in the unit circle that have this property are in the second and fourth quadrants.

The angle in the second quadrant is π - π/3 = 2π/3, and in the fourth quadrant, the angle is 2π - π/3 = 5π/3. Therefore, the solutions in radians within the given interval are 2π/3 and 5π/3.