Amplitude and Period Basics
A repeating wave has two simple traits. Amplitude shows height. Period shows cycle length. Together, they describe how strong and how long a motion is. The same ideas appear in sound, tides, pendulums, voltage, and trigonometry graphs.
Why These Values Matter
Amplitude tells how far a curve moves from its midline. A larger amplitude means a taller wave. Period tells how much horizontal distance is needed for one full repeat. A shorter period means the wave repeats faster. Frequency is the opposite of period. It counts cycles in one unit.
Using Equation Inputs
Many classroom problems use y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. The coefficient A controls amplitude. The coefficient B controls period. The value C moves the graph left or right. The value D sets the midline. This calculator accepts these values and reports each part in clear terms.
Using Maximum and Minimum Values
Some problems do not provide an equation. They only show a highest value and a lowest value. In that case, amplitude equals half of the total vertical range. The midline equals the average of the maximum and minimum. This method is useful when reading graphs or measured data.
Using Cycle Points
You can also enter the start and end of one full cycle. The distance between those points becomes the period. The calculator then finds frequency from that period. This helps when you know two matching points on a graph.
Checking Results
Always review the unit setting before using the result. Degree based graphs use 360 as the base cycle. Radian based graphs use 2π as the base cycle. Also check the sign of B. A negative value reflects the curve, but period stays positive.
Practical Use
This tool supports quick homework checks, graph planning, and waveform notes. It also creates export files for records. Use the table section to compare sample inputs. Then adjust the form values for your own problem.
Common Mistakes
Do not confuse amplitude with total height. The total height is double the amplitude. Do not use 180 for a full cycle. That only covers half of a sine or cosine repeat. Check signs and units before exporting final answers.