Graph PlottersExplore amplitude, period, phase shift, and vertical shift in an interactive sine graph built for homework and quick checks.
Hover to inspect coordinates. Drag the graph to pan the view or use the wheel and zoom controls to explore the function.
ABOUT THE TOOL
A sine wave repeats smoothly. In A sin(Bx + C) + D, |A| is the amplitude, 2π/|B| is the period in radians, −C/B is the phase shift, and D sets the midline.
HOW TO USE IT
The sine graph calculator uses y = A sin(Bx + C) + D as a visual study guide. The amplitude is |A|, the period is 2π/|B| in radians or 360°/|B| in degrees, the phase shift is −C/B, and D moves the midline. Change the coefficients directly or type a new expression, then watch the curve and summary cards update together. This makes it easier to tell whether a change affects height, repetition, horizontal position, or vertical position.
Trigonometry problems do not always use the same angle unit. Radians are common in algebra, precalculus, and calculus, while degrees appear frequently in introductory trigonometry. Use the angle selector to keep the displayed period consistent with your work. If the frequency is large, zoom out to see a useful number of cycles; there is no artificial limit on the numeric coefficients you enter.
Start with y = sin(x), try a negative amplitude, or add a vertical shift to move the midline. Hover over the graph to inspect coordinates around a crest, trough, or intercept. The tool is intentionally simple enough for a quick answer but detailed enough to support lessons about periodic functions, transformations, and the connection between an equation and its graph.
The parent sine function starts at the midline, rises to a maximum, returns through the midline, reaches a minimum, and repeats. In y = A sin(Bx + C) + D, the midline is y = D and the maximum and minimum are D + |A| and D − |A|. The sign of A can reflect the cycle, while |B| changes the spacing between matching points. These relationships let you sketch a sine graph before using the calculator and give you checkpoints for verifying a digital graph.
For y = 3 sin(2x − π/2) − 1, the amplitude is 3, the midline is y = −1, and the period is π radians. Factoring the input gives 2(x − π/4), so the phase shift is π/4 to the right. Plot the equation, check the first crest and trough against the expected midline and amplitude, and switch to degrees only when the original problem uses degrees.
For y = 2sin(3x − π/2) + 4, the amplitude is 2, the period is 2π/3, the phase shift is π/6 right, and the midline is y = 4. The range is therefore 2 ≤ y ≤ 6. Enter the expression, switch between radians and degrees only when appropriate, and compare the first crest and trough with these predicted values.
Sine functions are useful for quantities that repeat, such as a pendulum’s position, a seasonal measurement, or a simple sound wave. The midline represents the average level, amplitude represents the size of the variation, and period represents the time or distance for one full repetition. The calculator helps you connect those meanings to a plotted cycle rather than treating the parameters as isolated formulas.
Explore related tools as you study functions: start with the online graphing calculator to plot a general equation, then use the linear graph calculator for constant rates and the slope calculator for rise over run. When a curve meets the x-axis, check the x intercept calculator; for parabolas, compare the quadratic graph calculator and vertex calculator. Use the cubic graph calculator for polynomial end behavior, the sine graph calculator and cosine graph calculator for periodic models, and the phase shift calculator for horizontal movement. The function transformations calculator compares parent and transformed curves, while the absolute value graph calculator explains V-shaped graphs. For growth and inverse relationships, try the exponential growth graph calculator, reciprocal graph calculator, and log graph calculator. For asymptote and periodic-function practice, use the tangent graph calculator, secant graph calculator, and cosecant graph calculator to compare branches, gaps, and repeating behavior.
COMMON QUESTIONS
The amplitude is the absolute value of A. It measures the distance from the midline to a crest or trough.
The phase shift is π/2 units to the right.
Use the unit from your problem. Radians are common in algebra and calculus, while degrees are common in introductory trigonometry.
For y = A sin(Bx + C) + D, the range is D − |A| ≤ y ≤ D + |A|.
No. B changes the period and horizontal spacing. The amplitude is controlled by |A|.
One full cycle is 360° in degree mode but 2π radians in radian mode, so the numeric period uses the selected angle unit.