Solve the System of @WORD sin(x)>0 , cos(x)>0

Problem

{[sin(x)>0],[cos(x)>0])

Solution

1. Identify the quadrants where the sine function is positive. The condition sin(x)>0 is satisfied when the angle x is in the first or second quadrant.

2. Identify the quadrants where the cosine function is positive. The condition cos(x)>0 is satisfied when the angle x is in the first or fourth quadrant.

3. Determine the intersection of these two conditions. Both sin(x)>0 and cos(x)>0 are true only in the first quadrant.

4. Express the solution for the first quadrant in terms of radians. This corresponds to the interval (0,π/2)

5. Generalize the solution to account for the periodicity of the trigonometric functions by adding 2*k*π where k is any integer.

Final Answer

2*k*π<x<π/2+2*k*π,k∈ℤ

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