Explore sin, cos, tan and their inverses with amplitude, period, phase shift, and vertical shift sliders. Shows transformations live.
Drag a slider and the curve on the grid redraws while you drag. Pick sine, cosine, tangent, or one of the inverses, then set amplitude, period, phase shift, and vertical shift; the tool plots the transformed function for whatever combination you land on. It is a graphing board, not a solver - you read the consequences of each parameter off the curve. Two things surprise first-time users. Tangent has no amplitude: it has no peaks or troughs, and its period is pi, not 2pi. And the inverses are single-valued: selecting arcsin shows only the principal branch, not every angle with a given sine.
A concrete input and expected output from the current implementation.
Input
Function: sin. Sliders: amplitude 2, period pi, phase shift 0, vertical shift 1.
Expected output
Graph of f(x) = 2 sin(2x) + 1: one full cycle every pi units, midline at y = 1, peaks of 3 at x = pi/4 + k*pi and troughs of -1 at x = 3pi/4 + k*pi, so the curve stays between -1 and 3.
A period slider value of pi gives B = 2pi/pi = 2, so the curve completes one cycle between x = 0 and x = pi. Amplitude 2 stretches the sine swing from +/-1 to +/-2, and the vertical shift of +1 lifts the midline from 0 to 1, moving the range to [-1, 3].
The graph follows f(x) = A sin(B(x - C)) + D, and the four sliders set A, the period, C, and D. Amplitude A stretches the curve vertically; the period slider sets the distance for one full cycle, so B = 2pi/P; phase shift C slides the curve horizontally; vertical shift D moves the midline. For tangent the same form applies but the period is pi/B, half of sine's.
Choosing arcsin, arccos, or arctan switches the graph to the standard inverse curve. arcsin x and arccos x are defined only for x between -1 and 1, and the tool shows the branch returning angles in the principal ranges - [-pi/2, pi/2] for arcsin, [0, pi] for arccos. arctan x accepts any real input and returns values strictly between -pi/2 and pi/2. The sliders still transform these curves.
Direction depends on the formula convention. In the form A sin(B(x - C)) + D, increasing C shifts the graph right. In the older form A sin(Bx + phi), increasing phi shifts it left, because the effective shift is -phi/B. If the curve moves the unexpected way, check which form the tool's displayed formula uses before assuming a bug.
No. The inverse curves it plots are the single principal branches, so arcsin(0.5) shows only pi/6, roughly 0.524. The complete solution family - pi/6 + 2k*pi and 5pi/6 + 2k*pi - cannot be drawn as one function graph, and this tool does not enumerate it. For that, solve analytically or use a general equation solver.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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