Question

Plot the point with these polar coordinates. $$\left[1, \frac{1}{2} \pi\right]$$

Name: Problem 2, Chapter 10: Calculus: One Variable
Uploaded: 2021-08-04T13:06:05-08:00
Duration: 1 min 8 s
Channel: Sonam Khatri
Description: Plot the point with these polar coordinates. [1, (1)/(2) π]

   Plot the point with these polar coordinates.
$$\left[1, \frac{1}{2} \pi\right]$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 10, Problem 2

Instant Answer

Solved by Expert Sonam Khatri

08/04/2021

Step 1

The first number, 1, represents the distance from the origin (or pole). The second number, $\frac{1}{2}\pi$, represents the angle measured in radians from the positive x-axis (or initial line). Show more…

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Plot the point with these polar coordinates. $$\left[1, \frac{1}{2} \pi\right]$$

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Key Concepts

Polar Coordinates

Polar coordinates provide a method of locating points in a plane using a distance from a fixed point (the pole or origin) and an angle from a fixed direction (typically the positive x-axis). This system is especially useful for problems involving circular and rotational symmetry.

Radius and Angle

In the polar system, the point is determined by two values: the radius (r), which specifies the distance from the origin, and the angle (?), which specifies the direction relative to the positive x-axis. Understanding these components is essential for interpreting and plotting any point given in polar form.

Conversion to Cartesian Coordinates

To translate polar coordinates into the more familiar Cartesian (rectangular) coordinates, the equations x = r cos(?) and y = r sin(?) are used. This conversion is useful for visualizing the polar point within the standard x-y coordinate system.

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