What do A, B, C, and D do in y = A·sin(Bx + C) + D?
A is the amplitude (height), B sets the period as 360°/|B| (2π/|B| in radians), C produces a horizontal phase shift of −C/B, and D shifts the whole curve up or down to a new midline.
// maths › Trigonometric Functions & Graphs
Transformations: y = A·sin(Bx + C) + D
Explore how the four parameters in y = A sin(Bx + C) + D stretch, compress, and shift the sine curve — amplitude, period, phase shift, and vertical shift — with live sliders and a graph that redraws as you change each one, with the x-axis in degrees or radians.
y = A·sin(Bx + C) + D
Angle unit
Frequently asked questions
How do I find the period from B?
Divide 360° (or 2π radians) by the absolute value of B. So y = sin(2x) has period 360°/2 = 180° = π radians, completing two full waves in the space the basic sine does one.
Can you give a worked example?
For y = 2·sin(x), the amplitude is 2 and the period is 360° (2π rad). At x = 90° the value is 2·sin 90° = 2 — twice the height of the basic sine curve. Switch the toggle to see the x-axis in multiples of π.
What is a phase shift?
It is a horizontal slide of the curve, equal to −C/B. A positive C moves the wave to the left and a negative C moves it to the right, without changing its shape. It can be read in degrees or radians.
Where is this used in real life?
These transformations model real waves: tides (vertical shift for mean sea level), sound (amplitude for loudness, period for pitch), AC voltage, and daylight hours through the year.