Period Calculator
Find the period of y = A·sin(Bx + C) + D and describe the full wave properties.
Inputs
Period
2.094395
Frequency (cycles per unit)
0.477465
Amplitude
1.000000
Phase shift
-0.000000
Vertical shift (D)
0.0000
Step by step
Period formula
2π / |B| = 2π / |3|
= 2.0943951
Frequency
|B| / (2π) = |3| / (2π)
= 0.47746483
Amplitude
|A| = |1|
= 1
Phase shift
−C/B = −(0)/(3)
= 0
How it works
The period of y = A·sin(Bx + C) + D is 2π/|B| — the horizontal length of one complete cycle. Frequency is the reciprocal: |B|/(2π) cycles per x-unit.
Formula
Period
Period = 2π / |B|
- B
- Frequency coefficient
- T
- Period (one full cycle)
Frequently Asked Questions
What happens when B increases?
The period decreases (the wave compresses horizontally). B = 2 means 2 complete cycles in the interval [0, 2π].
How is period related to frequency?
Period = 1/frequency and frequency = 1/period. Period measures the length of one cycle; frequency measures cycles per unit.