1. What is the Sine Function?

The sine function is a fundamental trigonometric function that describes a smooth, periodic oscillation. It's widely used in mathematics, physics, engineering, and signal processing to model periodic phenomena.

2. How Does the Calculator Work?

The calculator uses the general sine function formula:

Where:

• \( a \) — Amplitude (peak deviation from center)
• \( b \) — Frequency (how many cycles occur in 2π radians)
• \( c \) — Phase shift (horizontal displacement)
• \( d \) — Vertical shift (up/down displacement)
• \( x \) — Input variable in radians

3. Parameters Explanation

Amplitude (a): Determines how tall the wave peaks are. Negative values flip the wave vertically.
Frequency (b): Controls how many complete cycles occur in 2π radians. Higher values mean more cycles.
Phase Shift (c): Moves the wave left or right. Positive values shift left, negative shift right.
Vertical Shift (d): Moves the entire wave up or down.

4. Using the Calculator

Tips: Enter the parameters and the x-range you want to graph. The calculator will generate 100 equally spaced points and plot the sine function.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sin(x) and cos(x)?
A: The cosine function is just a sine function shifted by π/2 radians (cos(x) = sin(x + π/2)).

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (1° ≈ 0.01745 radians).

Q3: What does a negative amplitude do?
A: It reflects the wave vertically (flips it upside down).

Q4: What's the period of the sine function?
A: The period is 2π/b radians. For b=1, it's 2π (about 6.28 radians).

Q5: Can I graph other trigonometric functions?
A: This calculator is specifically for sine functions, but cosine can be graphed by adding π/2 to the phase shift.