1. What is the Sine Function Equation?

The sine function equation describes a periodic oscillation. The general form is y = a·sin(bx + c) + d, where:

• a is the amplitude (peak deviation from center)
• b determines the period (2π/b)
• c is the phase shift (-c/b)
• d is the vertical shift

2. How Does the Calculator Work?

The calculator uses three points to solve for the parameters in the equation:

The system of equations is solved to find the values of a, b, c, and d that best fit the given points.

3. Importance of Sine Function

Details: Sine functions are fundamental in mathematics, physics, engineering, and signal processing for modeling periodic phenomena.

4. Using the Calculator

Tips: Enter three distinct points (x,y) in radians. For best results, choose points at different phases of the wave.

5. Frequently Asked Questions (FAQ)

Q1: How many points are needed to determine a sine function?
A: Three non-colinear points are theoretically sufficient, but more points improve accuracy.

Q2: What if my points don't perfectly fit a sine curve?
A: The calculator finds the best-fit sine function using least squares approximation.

Q3: Can I use degrees instead of radians?
A: The calculator expects x-values in radians. Convert degrees to radians first (radians = degrees × π/180).

Q4: What's the difference between sine and cosine?
A: Cosine is a phase-shifted sine: cos(x) = sin(x + π/2).

Q5: How is this used in real-world applications?
A: Sine functions model sound waves, light waves, alternating current, and many other periodic phenomena.