Convert to Interval Notation sin(x)>0

Problem

sin(x)>0

Solution

1. Identify the intervals where the sine function is positive within one full period. In the interval [0,2*π) the sine function is positive in the first and second quadrants.

sin(x)>0* for *0<x<π

2. Account for the periodicity of the sine function. Since sin(x) has a period of 2*π the inequality holds true for any interval shifted by an integer multiple of 2*π

2*π*n<x<π+2*π*n

3. Define the variable n as any integer to represent all possible intervals.

n∈ℤ

4. Convert the inequality to interval notation using parentheses to indicate that the endpoints are not included.

(2*π*n,π+2*π*n)

Final Answer

sin(x)>0⇒(2*π*n,π+2*π*n)* for all *n∈ℤ

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