Short Answer 
The distance between a star and the Sun is measured in astronomical units (AU), with one AU equivalent to approximately 93 million miles. Stellar parallax is used to calculate this distance through the sine function, leading to a result of 4124966.128 AU based on a small angular shift.
Step 1: Understanding Astronomical Units (AU)
Astronomers often measure vast distances in space using astronomical units (AU). One AU is defined as the average distance from the Earth to the Sun, approximately *93 million miles or 150 million kilometers*. In this context, the distance from the star to the Sun is 4124966.128 AU, which can be analyzed using trigonometric functions.
Step 2: Applying Stellar Parallax
The technique known as stellar parallax is crucial in measuring astronomical distances. For this, we utilize the sine function formulated as:
- sin θ = H / P
- Where H represents the hypotenuse and P is the perpendicular distance.
By employing this method, astronomers are able to calculate the distance to stars based on tiny angular shifts as viewed from different positions in Earth’s orbit.
Step 3: Calculating the Distance
To find the distance, we substitute the known angle into the sine equation. Given that θ = 0.00001389 degrees, we derive:
- sin(0.00001389) = d
Upon calculating and simplifying this expression, we arrive at the distance between the star and the Sun, which is 4124966.128 AU. This method showcases how mathematical functions can elucidate distances in the vast cosmos.