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What are the amplitude, period, frequency and initial phase in the mathematical trigonometric function?
The four terms you mentioned are used by comparing trigonometric functions we have learned with optics and electricity in physics.

The so-called amplitude refers to the maximum distance of the curve from the equilibrium position, that is, the number (absolute value) in front of sin.

Frequency is the number of times the curve appears repeatedly in 2π. Reflected in the trigonometric function is the coefficient ω of x.

The period is 2π divided by ω.

The initial phase is the function value when x is zero.

The above is actually in the textbook, so you must read it word for word, remember.

I won't go into details here.