Trigonometry: Difference between revisions
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where: | where: | ||
A, amplitude, the peak deviation of the function from zero. | A, amplitude, the peak deviation of the function from zero. | ||
f, ordinary frequency, the number of oscillations (cycles) that occur each second of time. | f, ordinary frequency, the number of oscillations (cycles) that occur each second of time. | ||
ω = 2πf, angular frequency, the rate of change of the function argument in units of radians per second | ω = 2πf, angular frequency, the rate of change of the function argument in units of radians per second | ||
φ , phase, specifies (in radians) where in its cycle the oscillation is at t = 0. | φ , phase, specifies (in radians) where in its cycle the oscillation is at t = 0. | ||
When φ is non-zero, the entire waveform appears to be shifted in time by the amount | When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance. | ||
φ/ω seconds. A negative value represents a delay, and a positive value represents an advance. | |||
Revision as of 17:38, 23 March 2020
While most people associate trigonometry with triangles, it is more useful in technical fields to consider the trigonometric functions as related to circles.
f(t) = Asin(2pft + s) = Asin(wt + s)
where:
A, amplitude, the peak deviation of the function from zero.
f, ordinary frequency, the number of oscillations (cycles) that occur each second of time.
ω = 2πf, angular frequency, the rate of change of the function argument in units of radians per second
φ , phase, specifies (in radians) where in its cycle the oscillation is at t = 0.
When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.