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Ch. 11 - Parametric Equations and Polar Coordinates
Hass - Thomas' Calculus 15th Edition
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Tutti i libri di testoHass 15th EditionCh. 11 - Parametric Equations and Polar CoordinatesProblema 11.3.6c
Capitolo 11, Problema 11.3.6c

Polar to Cartesian Coordinates


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


c. (0, π/2)

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1
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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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.
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Intro to Polar Coordinates

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.
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Convert Equations from Rectangular to Polar

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.
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Graphing The Derivative - Special Cases
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