Understanding Cosine Period
A cosine wave repeats after a fixed horizontal distance. That distance is called the period. The base function cos x repeats every 2π radians, or every 360 degrees. When the input becomes Bx + C, the coefficient B compresses or stretches the wave. A large absolute B makes the wave repeat faster. A small absolute B makes it repeat slowly.
Why The Period Matters
Period tells you how much x must change before the same height appears again. It is important in trigonometry, sound, motion, tides, signals, and classroom graphing. Students often confuse amplitude with period. Amplitude changes height only. Vertical shift moves the midline only. The period comes from the horizontal coefficient. This calculator separates those parts, so the answer is easier to check.
Advanced Inputs Explained
The calculator accepts the full model y = A cos(Bx + C) + D. A controls amplitude. B controls period and frequency. C creates a horizontal shift. D moves the midline. You may choose radians or degrees. You may also solve backward from a desired period. That option is useful when you need a cosine equation matching a known cycle length.
Reading The Results
The result panel shows the period, coefficient, frequency, amplitude, midline, maximum value, minimum value, half period, and quarter period. The phase shift is also displayed. It equals -C/B, so its sign depends on both values. The sample table starts at a cosine peak location. It then lists several x and y values across selected cycles. This makes graph checking faster.
Using The Output
Use the CSV button when you need spreadsheet data. Use the PDF button when you want a saved report. Keep enough decimals for your task. Rounding can slightly change graph points, especially near zeros. For exact math, keep π in your written solution when radians are used. For decimal reports, choose a precision that matches your assignment or measurement. Always confirm that B is not zero. A zero B removes the repeating horizontal change, so a normal period is not defined.
Avoid Mistakes
Do not divide by A when finding period. Do not use C alone as shift. Divide C by B with the opposite sign. Choose degrees only when the input angle uses degrees.