Solve tan⁡(3𝑥)=0 in the interval 0<𝑥<23𝜋Give your solution(s) correct to 2 decimal places where appropriate.

The equation tan(3x) = 0 has solutions where 3x is an integer multiple of π.

Step 1: Set 3x equal to nπ, where n is an integer.

3x = nπ

Step 2: Solve for x.

x = nπ/3

Step 3: Find the values of x in the interval 0 < x < 23π.

For n = 1, x = π/3 ≈ 1.05 For n = 2, x = 2π/3 ≈ 2.09 For n = 3, x = π ≈ 3.14 For n = 4, x = 4π/3 ≈ 4.19 For n = 5, x = 5π/3 ≈ 5.24 For n = 6, x = 2π ≈ 6.28 Continue this pattern until you reach the upper limit of the interval, 23π.

The solutions to the equation tan(3x) = 0 in the interval 0 < x < 23π are x = nπ/3 for n = 1, 2, 3, ..., up to n = 69.