Difference between revisions of "Trigonometry"
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(Created page with "While most people associate trigonometry with triangles, it is more useful in technical fields to consider the trigonometric functions as related to circles.") |
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While most people associate trigonometry with triangles, it is more useful in technical fields to consider the trigonometric functions as related to circles. | 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 {\displaystyle \varphi } | ||
| + | , phase, specifies (in radians) where in its cycle the oscillation is at t = 0. | ||
| + | |||
| + | When | ||
| + | φ {\displaystyle \varphi } | ||
| + | is non-zero, the entire waveform appears to be shifted in time by the amount | ||
| + | φ {\displaystyle \varphi } | ||
| + | /ω seconds. A negative value represents a delay, and a positive value represents an advance. | ||
Revision as of 17:36, 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 {\displaystyle \varphi } , phase, specifies (in radians) where in its cycle the oscillation is at t = 0.
When φ {\displaystyle \varphi }
is non-zero, the entire waveform appears to be shifted in time by the amount
φ {\displaystyle \varphi } /ω seconds. A negative value represents a delay, and a positive value represents an advance.
