What is the period of a sine graph?

The period is the horizontal length of one complete cycle, given by 2π / |B|. For y = sin(x), B = 1 so the period is 2π. Doubling B to 2 halves the period to π, packing two waves into the same width, while B = 0.5 stretches the period to 4π. Tangent is the exception: its period is π / |B|.

What is the difference between a sine and cosine graph?

They are the same wave shifted horizontally. Cosine starts at its peak — cos(0) = 1 — while sine starts at zero and rises. Formally cos(x) = sin(x + π/2), so cosine is sine shifted a quarter-period to the left. Both share the same amplitude, period, and midline.

How do you graph a tangent function?

Tangent equals sin(x) / cos(x), so it has vertical asymptotes wherever cos(x) = 0 — at π/2, 3π/2, and every odd multiple of π/2. Between asymptotes the curve climbs from −∞ to +∞, crossing zero at each multiple of π, with a period of π. This tool draws each branch separately and marks the asymptotes as dashed vertical lines.

What do amplitude, period, phase shift, and vertical shift mean?

In y = A·sin(B(x − C)) + D: amplitude A is the vertical stretch (distance from the midline to a peak); B sets the period via 2π / |B|; phase shift C slides the wave horizontally (right for positive C); and vertical shift D moves the midline up or down to y = D. Change any one in the tool to see its effect instantly.

Can I download or print the trig graph?

Yes. The precise mode exports a clean SVG or a high-resolution PNG (rendered at 2x) that drops neatly into worksheets, slides, and homework. Precise mode runs entirely in your browser and does not use image-generation credits.

Math Tool

Sine Graph Generator Sin, Cos & Tan

Q: How do I graph a sine function?

Enter the amplitude (A), B (which sets the period), phase shift (C), and vertical shift (D) for y = A·sin(B(x − C)) + D. The precise mode instantly plots a smooth wave with the x-axis labeled in radians using π-fractions, marks the midline and amplitude, and reports the period. Adjust the graph window so at least one full cycle is visible, then export SVG or PNG.

Graph sine, cosine, and tangent functions with amplitude, period, phase shift, and vertical shift. Radians or degrees, labeled in π. Export SVG or PNG.

Graph sine, cosine & tangent exactlyAmplitude, period, phase & vertical shiftX-axis labeled in radians (π-fractions)SVG & PNG export

Function

y = A · sin(B · (x − C)) + D

Amplitude (A)B (period)Phase shift (C)Vertical shift (D)

Angle mode

Graph window

X minX maxY minY max

Midline (y = D)Amplitude (max/min)

Readout

y = sin(x)

Period: 2π
Amplitude: 1
Midline: y = 0

Trig Graph Examples

Common ways to graph and label sine, cosine, and tangent functions

View:

Labeled Sine Graph

A standard sine wave on a coordinate plane with the x-axis labeled in π-fractions.

sinelabeled

Cosine Graph

A cosine wave starting at its maximum value of 1 when x = 0.

cosine

Amplitude and Period

A stretched sine wave with its amplitude and one full period highlighted.

amplitudeperiod

Phase Shift

A sine wave shifted horizontally to illustrate a phase (horizontal) shift.

phase-shift

Tangent Graph

A tangent graph with its repeating branches and dashed vertical asymptotes.

tangentasymptotes

Sine vs Cosine

A sine wave and a cosine wave drawn together to compare their shapes.

sinecosine

What is a sine graph?

A sine graph is the smooth, repeating wave you get when you plot y = sin(x). As x increases, the value of sine rises and falls forever between −1 and 1, tracing a curve that crosses the x-axis at every multiple of π. A standard sine wave passes through the origin (0, 0), reaches its peak of +1 at x = π/2, returns to 0 at x = π, dips to its lowest point of −1 at x = 3π/2, and completes one full cycle back at 2π. Because the pattern repeats, sine (and its cousins cosine and tangent) describe anything that oscillates: sound waves, alternating current, tides, springs, and light. This generator plots all three trigonometric functions exactly from their equation, with the x-axis labeled in radians using π-fractions so the graph matches what you see in a textbook.

Amplitude, period, phase shift, and vertical shift

Every sine or cosine curve can be written as y = A·sin(B(x − C)) + D, and each letter transforms the basic wave in a specific way.
A is the amplitude — the vertical stretch. It is the distance from the midline up to a peak (or down to a trough), so y = 2 sin(x) rises to +2 and falls to −2. A negative A flips the wave upside down.
B controls the period, the horizontal length of one full cycle, through the formula period = 2π / |B|. A larger B squeezes more waves into the same space: B = 2 halves the period to π, while B = 0.5 doubles it to 4π.
C is the phase shift, a horizontal slide. Writing (x − C) moves the whole wave C units to the right (or left when C is negative). D is the vertical shift, which raises or lowers the midline to y = D. Together, A, B, C, and D let you match any sinusoid.

Sine vs cosine

Sine and cosine are the same wave shifted horizontally. The cosine graph y = cos(x) starts at its maximum: at x = 0 it equals +1, then falls to 0 at π/2, to −1 at π, and back to +1 at 2π. Sine, by contrast, starts at 0 and rises first.
In fact cos(x) = sin(x + π/2), so cosine is simply sine shifted a quarter-period to the left. Both have the same amplitude, period, and midline — only the starting point differs. Switching the function selector between sin and cos in this tool shows the two curves side by side.
Knowing this relationship makes graphing faster: sketch a sine wave, and you already know the cosine wave is the same curve nudged over by π/2.

Graphing tangent and its asymptotes

Tangent behaves very differently from sine and cosine. Because tan(x) = sin(x) / cos(x), the function shoots off to infinity wherever cos(x) = 0 — at x = π/2, 3π/2, and every odd multiple of π/2. At those x-values the graph has a vertical asymptote, a line the curve approaches but never touches.
Between consecutive asymptotes the tangent curve rises from −∞ to +∞, passing through zero at every multiple of π. Its period is π (not 2π), so the branches repeat twice as often as a sine wave. This tool draws each branch as a separate piece and marks the asymptotes as dashed vertical lines, so the curve never appears to jump straight across the gap.
When you graph tangent, the amplitude and midline controls do not apply the same way — there is no maximum or minimum to mark — so the tool hides those markers and shows the asymptotes instead.

Tips for graphing trig functions

Start by identifying A, B, C, and D from the equation before you draw. Find the period with 2π / |B|, mark the midline y = D, then place the peaks and troughs one amplitude above and below it.
Choose an x-window that shows at least one full period — for a standard wave, −2π to 2π works well and lines up neatly with the π-fraction ticks. Widen the y-window for tall amplitudes so the peaks are not clipped.
Use the presets to see the four canonical cases instantly, then tweak one parameter at a time to build intuition for how each transformation changes the wave. Export a clean SVG or PNG for worksheets, slides, and homework.

Frequently Asked Questions

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Sine Graph Generator Sin, Cos & Tan

Graph sine, cosine, and tangent functions with amplitude, period, phase shift, and vertical shift. Radians or degrees, labeled in π. Export SVG or PNG.

Graph sine, cosine & tangent exactlyAmplitude, period, phase & vertical shiftX-axis labeled in radians (π-fractions)SVG & PNG export

What is a sine graph?

Amplitude, period, phase shift, and vertical shift

Every sine or cosine curve can be written as y = A·sin(B(x − C)) + D, and each letter transforms the basic wave in a specific way.

A is the amplitude — the vertical stretch. It is the distance from the midline up to a peak (or down to a trough), so y = 2 sin(x) rises to +2 and falls to −2. A negative A flips the wave upside down.

B controls the period, the horizontal length of one full cycle, through the formula period = 2π / |B|. A larger B squeezes more waves into the same space: B = 2 halves the period to π, while B = 0.5 doubles it to 4π.

C is the phase shift, a horizontal slide. Writing (x − C) moves the whole wave C units to the right (or left when C is negative). D is the vertical shift, which raises or lowers the midline to y = D. Together, A, B, C, and D let you match any sinusoid.

Sine vs cosine

Sine and cosine are the same wave shifted horizontally. The cosine graph y = cos(x) starts at its maximum: at x = 0 it equals +1, then falls to 0 at π/2, to −1 at π, and back to +1 at 2π. Sine, by contrast, starts at 0 and rises first.

In fact cos(x) = sin(x + π/2), so cosine is simply sine shifted a quarter-period to the left. Both have the same amplitude, period, and midline — only the starting point differs. Switching the function selector between sin and cos in this tool shows the two curves side by side.

Knowing this relationship makes graphing faster: sketch a sine wave, and you already know the cosine wave is the same curve nudged over by π/2.

Graphing tangent and its asymptotes

Tangent behaves very differently from sine and cosine. Because tan(x) = sin(x) / cos(x), the function shoots off to infinity wherever cos(x) = 0 — at x = π/2, 3π/2, and every odd multiple of π/2. At those x-values the graph has a vertical asymptote, a line the curve approaches but never touches.

Between consecutive asymptotes the tangent curve rises from −∞ to +∞, passing through zero at every multiple of π. Its period is π (not 2π), so the branches repeat twice as often as a sine wave. This tool draws each branch as a separate piece and marks the asymptotes as dashed vertical lines, so the curve never appears to jump straight across the gap.

When you graph tangent, the amplitude and midline controls do not apply the same way — there is no maximum or minimum to mark — so the tool hides those markers and shows the asymptotes instead.

Tips for graphing trig functions

Start by identifying A, B, C, and D from the equation before you draw. Find the period with 2π / |B|, mark the midline y = D, then place the peaks and troughs one amplitude above and below it.

Choose an x-window that shows at least one full period — for a standard wave, −2π to 2π works well and lines up neatly with the π-fraction ticks. Widen the y-window for tall amplitudes so the peaks are not clipped.

Use the presets to see the four canonical cases instantly, then tweak one parameter at a time to build intuition for how each transformation changes the wave. Export a clean SVG or PNG for worksheets, slides, and homework.