AmplitudeThe height from the midline to a maximum. The letter A sets it: here A is 2.
PeriodThe length of one full cycle. It is 2π divided by B: here B is 1, so the period is 2π.
Phase shiftHow far the curve is moved sideways. The letter C sets it: here a cycle starts at π/2, not at 0.
Vertical shiftHow far the curve is moved up or down. The letter D sets it: here the midline is 3 above the x-axis.
On the curve 3
MidlineThe level line halfway between the tops and the bottoms. Its equation is y = D, here y = 3.
MaximumA highest point of the curve. Its height is the midline plus the amplitude: 3 + 2 = 5.
MinimumA lowest point of the curve. Its height is the midline minus the amplitude: 3 − 2 = 1.
How this list was compiled: Every name was read on 2026-10-03 in at least two of these. (1) Ted Sundstrom and Steven Schlicker, Trigonometry, Grand Valley State University, section 2.2 Graphs of Sinusoidal Functions, https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/02%3A_Graphs_of_the_Trigonometric_Functions/2.02%3A_Graphs_of_Sinusoidal_Functions (the form y = A sin(B(t − C)) + D; the amplitude is |A|; the period is 2π divided by B; a horizontal translation of a sinusoid is called a phase shift, C units to the right when C is positive; the vertical shift is D; the level line y = D is the center line; high and low points). (2) Matthew Boelkins, Active Prelude to Calculus, section 2.4 Sinusoidal Functions, https://activecalculus.org/prelude/sec-circular-sinusoidal.html (midline, amplitude and period of a sine curve; a sin(k(t − b)) + c as a horizontal shift by b, a vertical stretch by a and a vertical shift of c, with k equal to 2π divided by the period; minimum and maximum values). (3) California Department of Education, California Common Core State Standards: Mathematics, https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf (trigonometric functions graphed showing period, midline and amplitude; relative maximums and minimums). (4) Wikipedia, English edition: Sine wave, https://en.wikipedia.org/wiki/Sine_wave (amplitude as the peak deviation of the function), Phase (waves), https://en.wikipedia.org/wiki/Phase_(waves) (phase shift) and Sinusoidal model, https://en.wikipedia.org/wiki/Sinusoidal_model (a constant mean level, an amplitude and a phase shift). (5) Carl Stitz and Jeff Zeager, Precalculus, an open-license text, section 10.5 Graphs of the Trigonometric Functions, https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/10%3A_Foundations_of_Trigonometry/10.05%3A_Graphs_of_the_Trigonometric_Functions (four properties describe a sinusoid: its period, amplitude, phase shift and vertical shift; for A sin(ωx + φ) + B the period is 2π divided by ω, the amplitude |A|, the phase shift −φ divided by ω and the vertical shift B, which gives C and D for the form used here). Hints, detail lines and the example are our own. Licence: own work
The drawing: Drawn for this site by script from the equation, 2026-10-03. Own work. Licence: own work
How it works
This sine graph equation labeled chart prints y = A sin(B(x − C)) + D above a curve. It marks the amplitude, period, phase shift and vertical shift that the letters set, then the midline, a maximum and a minimum.
Read the full guide
Match each letter
Four parts are set by a letter of the equation. A sets the amplitude. B sets the period, which is 2π divided by B. C is the phase shift and D is the vertical shift. The curve drawn is y = 2 sin(x − π/2) + 3.
Read the curve
The dashed midline is at y = 3. The curve rises 2 above it to each maximum and falls 2 below it to each minimum. One cycle starts at π/2, at the dot on the midline, and the next starts 2π later.
Amplitude is measured from the midline, not from the x-axis.
Questions and answers
What do A, B, C and D mean in a sine equation?
In y = A sin(B(x − C)) + D, A sets the amplitude, B sets the period, C is the phase shift and D is the vertical shift. The amplitude is the size of A without its sign.
How do you find the period of a sine graph?
On the graph, measure the length of one full cycle, such as the distance from one maximum to the next. From the equation, divide 2π by B.
What is the midline of a sine graph?
The level line halfway between the maximums and the minimums. In y = A sin(B(x − C)) + D it is the line y = D.
What is the phase shift of a sine graph?
How far the curve is moved sideways. In the form y = A sin(B(x − C)) + D it is C: to the right when C is positive, to the left when C is negative. Here C is π/2.