Convert the rectangular coordinates left parenthesis, 0, comma, 5, square root of, 2, end square root, right parenthesis(0,5 2 ) into polar form. Express the angle using radians in terms of piπ over the interval 0, is less than or equal to, theta, is less than, 2, pi0≤θ<2π, with a positive value of rr.
Question
Convert the rectangular coordinates left parenthesis, 0, comma, 5, square root of, 2, end square root, right parenthesis(0,5 2 ) into polar form. Express the angle using radians in terms of piπ over the interval 0, is less than or equal to, theta, is less than, 2, pi0≤θ<2π, with a positive value of rr.
Solution
The rectangular coordinates given are (0, 5√2).
Step 1: Find the radius (r) The radius in polar coordinates is given by the formula r = √(x² + y²). Here, x = 0 and y = 5√2.
So, r = √((0)² + (5√2)²) = √(0 + 50) = √50 = 5√2.
Step 2: Find the angle (θ) The angle in polar coordinates is given by the formula θ = atan(y/x). But here, x = 0, so the formula is not directly applicable.
However, we know that when x = 0, the angle θ is either π/2 or 3π/2 depending on the sign of y. Since y = 5√2 is positive, θ = π/2.
So, the polar coordinates are (5√2, π/2).
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