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# Sketch in Standard Position Calculator Online

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The Sketch in Standard Position Calculator converts Cartesian coordinates (x, y) into polar coordinates (r, theta). This transformation helps in visualizing and solving problems related to the position of points in a plane. By inputting the Cartesian coordinates into the calculator, users can quickly find the radius and angle, making complex calculations simple and accessible.

## Formula of Sketch in Standard Position Calculator

To find the standard position of a sketch, use these formulas:

#### Calculate the radius (r):

r = sqrt(x^2 + y^2)

#### Calculate the angle (theta):

theta = tan^(-1)(y/x)

These formulas convert the Cartesian coordinates (x, y) to polar coordinates (r, theta). The radius (r) represents the distance from the origin to the point, while the angle (theta) shows the direction from the positive x-axis to the point.

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## Pre-Calculated Values Table

Here is a table with common pre-calculated values for reference:

This table serves as a quick reference for commonly encountered coordinates, eliminating the need for repetitive calculations.

## Example of Sketch in Standard Position Calculator

Let’s go through an example to understand the application of these formulas.

#### Example:

Suppose we have the Cartesian coordinates (3, 4).

1. Calculate the radius (r): r = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5
2. Calculate the angle (theta): theta = tan^(-1)(4/3) ≈ 53.13°