Find the Quadrant (3,pi/3)

Problem

(3,π/3)

Solution

1. Identify the given coordinates as polar coordinates (r,θ) where r=3 and θ=π/3

2. Determine the value of the angle θ in degrees to visualize the position.

θ=π/3⋅180^∘/π

θ=60^∘

3. Locate the quadrant based on the standard angle ranges: Quadrant I (0<θ<90^∘, Quadrant II (90^∘<θ<180^∘, Quadrant III (180^∘<θ<270^∘, and Quadrant IV (270^∘<θ<360^∘.

4. Conclude that since 60^∘ falls between 0^∘ and 90^∘ and the radius r is positive, the point lies in the first quadrant.

Final Answer

(3,π/3)⇒Quadrant I

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