Convert the rectangular coordinates left parenthesis, 0, comma, 1, right parenthesis(0,1) 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, 1, right parenthesis(0,1) 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 (0,1) can be converted into polar form using the following steps:
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Calculate the radius r: The radius r in polar coordinates is given by the formula r = sqrt(x^2 + y^2). For the point (0,1), r = sqrt(0^2 + 1^2) = 1.
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Calculate the angle θ: The angle θ in polar coordinates is given by the formula θ = atan(y/x). However, since x = 0 in this case, we cannot use this formula directly as it would result in a division by zero. Instead, we need to consider the quadrant in which the point lies. The point (0,1) lies on the positive y-axis, so θ = π/2.
Therefore, the polar coordinates of the point (0,1) are (1, π/2).
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