Trigonometry · interactive lab
Sine & cosine graph explorer
See amplitude, period, phase shift, and vertical shift change a wave in real time.
Sine & cosine graph explorerLIVE EXPLORATION
Change a value to see the connection
Your measurements
The graph spans −2π to 2π on the x-axis. x and h are measured in radians.
Why it works
y = A sin(B(x − h)) + k
A little question. A clearer picture.
Sine & cosine graph explorer: common questions
Wondering about the why? Start here.
What do amplitude and period mean?
Amplitude is the distance from a wave’s midline to a peak. In y = A sin(B(x − h)) + k, amplitude is |A| and the period is 2π/|B| for nonzero A and B. This explorer uses nonnegative A and positive B. When A is zero, the graph is constant and has no unique fundamental period.
Explore the wave parametersHow do phase shift and vertical shift move the graph?
In y = A sin(B(x − h)) + k, a positive h moves the graph right and a negative h moves it left. The value k moves the midline to y = k. Here, horizontal values and phase shift are measured in radians.
See graph transformation examples