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.