Convert to Interval Notation tan(x)> = square root of 3

Problem

tan(x)≥√(,3)

Solution

1. Identify the base angle by finding the value of x in the first quadrant where tan(x)=√(,3)

tan(x)=√(,3)⇒x=π/3

2. Determine the interval within one period of the tangent function, which is (−π/2,π/2) Since the tangent function is increasing on this interval, tan(x)≥√(,3) when x is between π/3 and the vertical asymptote at π/2

π/3≤x<π/2

3. Account for periodicity by adding n*π to the endpoints, where n is any integer, because the tangent function repeats every π radians.

π/3+n*π≤x<π/2+n*π

4. Express in interval notation using brackets for included values and parentheses for excluded values (asymptotes).

[π/3+n*π,π/2+n*π)

Final Answer

tan(x)≥√(,3)=(⋃_n∈ℤ^)(π/3+n*π,π/2+n*π)

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