Polar to Cartesian Coordinates

Find the Cartesian coordinates of the following points, given in polar coordinates.

c. (0, π/2)

검증된 단계별 안내

Recall the formulas to convert from polar coordinates \((r, \theta)\) to Cartesian coordinates \((x, y)\):

\[x = r \cdot \cos(\theta)\]

\[y = r \cdot \sin(\theta)\]

Substitute the given polar coordinates \((r, \theta) = (0, \frac{\pi}{2})\) into the formulas:

Calculate the values of \(x\) and \(y\) using the substituted values without simplifying the final numeric result.

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주요 개념

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Polar Coordinates

Polar coordinates represent a point in the plane using a radius and an angle, denoted as (r, θ). The radius r is the distance from the origin, and θ is the angle measured from the positive x-axis, usually in radians.

Conversion Formulas from Polar to Cartesian

To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the formulas x = r * cos(θ) and y = r * sin(θ). These relate the radius and angle to horizontal and vertical distances.

Special Case: Zero Radius

When the radius r is zero, the point is at the origin regardless of the angle θ. This means the Cartesian coordinates are always (0, 0) for any angle if r = 0.

Polar to Cartesian CoordinatesFind the Cartesian coordinates of the following points, given in polar coordinates.c. (0, π/2)