Calculate properties of y = A sin(ωx + φ) and y = A cos(ωx + φ) including period, range, extrema, symmetry, and monotonic intervals.
Function Parameters
Configure your composite trigonometric function (A > 0, ω > 0)
A > 0
ω > 0
Any real
Current Function:
y = 1 sin(1x + 0)
Parameter Effects
Amplitude (A): Controls the vertical stretch. The function's range becomes [-A, A]. Larger A means taller waves.
Frequency (ω): Controls the horizontal compression. Period = 2π/ω (or 360°/ω). Larger ω means faster oscillation.
Phase (φ): Controls horizontal shift. Positive φ typically shifts left, negative φ shifts right (depending on the form).
Function Graph
Dynamically displays the graph of y = 1 sin(1x + 0), including key point markers
Sine Function
• Dots indicate key points (extrema and zeros)
Graph range: 0 to 4π. The graph updates in real-time as parameters change.
Calculation Methods
Period: For y = A sine(ωx + φ), T = 2π/ω (radians) or 360°/ω (degrees)
Extrema: Solve ωx + φ = key angles where sine reaches ±1
Symmetry: Use standard sine symmetry patterns, adjusted by transformations
Monotonicity: Analyze where derivative is positive/negative using chain rule
Note: All formulas use general form with integer k. The phase shift depends on how you interpret the function form. Results show standard mathematical conventions.
Related Resources
Frequently Asked Questions
This is the general form of a sinusoidal function where A is the amplitude (vertical stretch), ω affects the period (T = 2π/ω), and φ is the phase shift (horizontal translation).