1. What is the Sine Function?

The sine function is a fundamental trigonometric function that relates the angle θ in a right triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse. When given coordinates (x,y), it can be calculated as y divided by the radius (distance from origin).

2. How Does the Calculator Work?

The calculator uses the sine function formula:

Where:

• \( x \) — Horizontal coordinate
• \( y \) — Vertical coordinate
• \( r \) — Radius (distance from origin to point)
• \( \theta \) — Angle formed with positive x-axis

Explanation: The sine of the angle is calculated by taking the y-coordinate and dividing it by the distance from the origin to the point (x,y).

3. Importance of Sine Calculation

Details: The sine function is essential in mathematics, physics, engineering, and many other fields. It's used in wave analysis, circular motion, alternating current calculations, and more.

4. Using the Calculator

Tips: Enter the x and y coordinates of your point. Both values must be valid numbers. The calculator will compute the sine of the angle formed by the line from the origin to your point and the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What range of values can sine take?
A: The sine function always returns values between -1 and 1, inclusive.

Q2: What if both x and y are zero?
A: The origin point (0,0) doesn't form a valid angle, so sine is undefined in this case.

Q3: How is this different from regular sine calculation?
A: This method calculates sine directly from coordinates without needing to know the angle itself.

Q4: Can I use this for 3D coordinates?
A: No, this calculator is for 2D coordinates only. 3D calculations require additional z-coordinate considerations.

Q5: What's the relationship with cosine?
A: Cosine would be calculated as x/r using the same coordinates, giving the adjacent/hypotenuse ratio.