Sine to Unit Circle Coordinates Converter

How to Convert Sine to Unit Circle Coordinates

The unit circle is a circle with a radius of 1. When given a sine value, we can calculate the corresponding unit circle coordinates. The formula is:

Formula:

Coordinates = (cos(θ), sin(θ))

For a given sine value, you can use the inverse sine (arcsine) to calculate the angle, and then use cosine to find the x-coordinate.

Example:

Suppose sin(θ) = 0.5

Step 1: Apply the inverse sine function → asin(0.5) = 0.5236 radians

Step 2: Calculate cosine for the angle → cos(0.5236) = 0.866

Step 3: Unit Circle Coordinates → (0.866, 0.5)

Result: The coordinates are (0.866, 0.5).