Sine & Cosine Graph Calculator

A sinusoidal graph is a smooth repeating wave described by y = A sin(Bx + C) + D. A sets the height, B the period, C the horizontal shift and D the midline. This calculator works out each of these features, gives the maximum, minimum and range, and draws two full periods of the wave.

How to use the sine & cosine graph calculator

Choose sine or cosine.
Enter A, B, C and D (π is allowed, e.g. -pi/4).
Press Calculate to see the features and the graph.

Formula

y = A\sin(Bx + C) + D

\text{Period} = \frac{2\pi}{|B|}

Worked example: y = 3 sin(2x) + 1

Function: y = A sin(Bx + C) + D
A (amplitude): 3
B: 2
C: 0
D (vertical shift): 1

✓ Answer checked

\text{Amplitude} = 3,\; \text{Period} = \pi,\; \text{Phase shift} = 0,\; \text{Midline } y = 1

Maximum / minimum: $4 \;/\; -2$
Range: $[-2,\; 4]$
Frequency (cycles per unit): $0.31830989$

Two full periods. Orange dashed: midline y = 1. Green dashed lines are one period (3.1416) apart.

Step-by-step working (4 steps)

Amplitude
The amplitude is |A|: how far the wave goes above and below the midline.
$|A| = 3$
Period Period = 2π/|B|
One full cycle of sin or cos is 2π; dividing by |B| squeezes or stretches it.
$\frac{2\pi}{|B|} = \frac{2\pi}{2} = \pi$
Phase shift
Solve Bx + C = 0: the graph starts its cycle there.
$x = -\frac{C}{B} = 0$
Vertical shift
D moves the midline up or down.
$y = 1$