Graphing Sets of Polar Coordinate Points

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises 11–26.

θ = π/2, r ≥ 0

검증된 단계별 안내

Understand the polar coordinate system: each point is represented by \((r, \theta)\), where \(r\) is the distance from the origin and \(\theta\) is the angle measured from the positive x-axis.

Given the equation \(\theta = \frac{\pi}{2}\), this means all points lie along the line where the angle is \(90^\circ\), which corresponds to the positive y-axis in Cartesian coordinates.

The inequality \(r \geq 0\) means we only consider points at a distance \(r\) from the origin that are zero or positive, so points start at the origin and extend outward along the line \(\theta = \frac{\pi}{2}\).

To graph this, draw a ray starting at the origin and extending straight up along the positive y-axis, including the origin itself since \(r\) can be zero.

Label the ray to indicate that it corresponds to \(\theta = \frac{\pi}{2}\) and \(r \geq 0\), representing all points on this line from the origin upwards.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Polar Coordinates System

The polar coordinate system represents points in a plane using a radius and an angle. Each point is defined by (r, θ), where r is the distance from the origin and θ is the angle measured from the positive x-axis. This system is useful for graphing curves and points that are naturally circular or angular.

Graphing Lines in Polar Coordinates

In polar coordinates, the equation θ = constant represents a straight line through the origin at the specified angle. For θ = π/2, the line is vertical, corresponding to the positive y-axis in Cartesian coordinates. Points on this line have varying r values but a fixed angle.

Inequalities in Polar Coordinates

Inequalities like r ≥ 0 restrict the set of points to those with non-negative radius values. Since r represents distance, r ≥ 0 includes all points on or in front of the origin along the line θ = π/2. Negative r values would reflect points in the opposite direction.

Graphing Sets of Polar Coordinate PointsGraph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises 11–26.θ = π/2, r ≥ 0