Trigonometric Functions Calculator — Plot & Analyse sin, cos, tan and More
Explore any of the six trigonometric functions — sin, cos, tan, csc, sec, cot — with custom amplitude A, frequency multiplier k and phase shift φ. The calculator plots f(x) = A · fn(kx + φ) and computes the period, frequency, and key values at standard angles.
Trigonometric function
degrees
= 6.283185 rad • Frequency 0.159155 cycles/rad
- 1
Absolute frequency multiplier
|k| = |1| = 1 - 2
Period in radians
2π ÷ 1 = 6.283185One full cycle of the base trig function spans 2π radians. - 3
Period in degrees
6.283185 × (180 ÷ π) = 360
How does this calculator work?
f(x) = A · fn(kx + φ°). Period = 360°/|k| (sin, cos, csc, sec) or 180°/|k| (tan, cot). Amplitude = |A|. Phase shift φ slides the graph horizontally. Enter amplitude, frequency multiplier and phase shift to see the function plotted across three periods, plus period, frequency and key angle values.
Formula
How this is calculated
A sinusoidal function f(x) = A · sin(kx + φ) has three adjustable parameters. The amplitude A is the peak absolute value — it scales the graph vertically; a negative A flips it. The frequency multiplier k compresses or stretches the horizontal scale: period = 2π/|k| radians (or 360°/|k| in degrees), so k = 2 halves the period and k = 0.5 doubles it. The phase shift φ (in degrees here) slides the graph left or right — a positive φ shifts it to the left.
The graph is plotted from −360° to 720° (covering three full periods at k = 1) by sampling 400 points. For functions with vertical asymptotes (tan, csc, sec, cot), the plot is split at each asymptote into separate line segments; values beyond 6 × |A| are clipped to keep the axis scale readable. The period is always 360°/|k| for all six functions; cosecant and secant share the period of sine and cosine, while cotangent shares the period of tangent (180°/|k|).
The wave animation shows a stylised sine (or cosine) wave for orientation; the main XYPlot shows the actual function with your parameters applied.
Frequently asked questions
Amplitude A is the maximum distance from the midline — the graph peaks at A and troughs at −A. Period is the length of one complete cycle — 360°/|k| for sin/cos. Phase shift φ moves the entire graph horizontally without changing its shape. Together they fully describe any sinusoidal wave in physics, engineering and signal processing.
Tangent repeats every 180° (π radians), not 360°, because tan(θ + 180°) = tan θ. The same is true of cotangent. Sine and cosine need the full 360° to complete their cycle. When using the frequency multiplier k, tan's effective period is 180°/|k|.
Csc = 1/sin is undefined wherever sin = 0 (at 0°, 180°, 360°, …). Sec = 1/cos is undefined wherever cos = 0 (at 90°, 270°, …). Cot = cos/sin is undefined wherever sin = 0. At these angles the denominator is zero and the function approaches ±∞, creating vertical asymptotes on the graph.
Also known as
TG we-Calculate Editorial Team. (2026). Trigonometric Functions Calculator — Plot & Analyse sin, cos, tan and More [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trigonometric-functions-calculator
TG we-Calculate Editorial Team. "Trigonometric Functions Calculator — Plot & Analyse sin, cos, tan and More." TG we-Calculate. 2026. https://we-calculate.com/calculator/trigonometric-functions-calculator.
TG we-Calculate Editorial Team, "Trigonometric Functions Calculator — Plot & Analyse sin, cos, tan and More," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trigonometric-functions-calculator
@misc{wecalculate_trigonometric_functions_calculator, title = {Trigonometric Functions Calculator — Plot & Analyse sin, cos, tan and More}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trigonometric-functions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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