Circular functions and their graphs: Interactive graph of sine, cosine and tangent on −2π to 2π with controls for amplitude, period, phase shift and vertical shift

Cosine is just sine running π/2 ahead

Every letter in y = a sin(n(x − h)) + k is a move you can point to on the graph: a sets the height, n sets how many waves fit, h slides the wave sideways and k lifts the midline. Switch between sin, cos and tan, then raise n and watch what happens to the width of one wave between −2π and 2π.

Graph range [−1, 1]
Switch the function. Raise n and watch the dashed bracket. Push a below zero and watch the first turning point after x = 0.
Function
y = sin(x)
a · vertical stretch1
−3 −1.5 0 1.5 3
n · coefficient of x1
0.5 1 1.5 2 2.5 3
h · phase shift0
−π −π/2 0 π/2 π
k · vertical shift0
−2 −1 0 1 2
Amplitude |a|
1
midline y = 0
Period 2π/n
2π
≈ 6.28
Reading the graph
Know This
In y = a sin(n(x − h)) + k the amplitude is |a| and the period is 2π/n, with the midline at y = k; tan has no amplitude and repeats every π/n.