Graph cos(theta)>0

Problem

cos(θ)>0

Solution

1. Identify the condition where the cosine function is positive. On the unit circle, cos(θ) represents the xcoordinate of a point.

2. Determine the quadrants where the xcoordinate is positive. This occurs in Quadrant I and Quadrant IV.

3. Find the interval of angles for one full rotation. The cosine function is positive when −π/2<θ<π/2

4. Generalize the solution for all rotations by adding multiples of 2*π The inequality holds for θ in the intervals (2*n*π−π/2,2*n*π+π/2) for any integer n

5. Visualize the graph on a coordinate plane where the horizontal axis is θ and the vertical axis is y=cos(θ) The solution consists of the regions where the cosine curve is strictly above the θaxis.

Final Answer

θ∈(⋃_n∈ℤ^)(2*n*π−π/2,2*n*π+π/2)

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