Find the amplitude, period, and phase shift of the function, and graph one complete period. y=2

step 1 given y is equal to 2 sign 2 by 3 x minus pi by 6 so this can be written as 2 into sign 2 by 3 t

Find the amplitude, period, and phase shift of the function,...

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Key Concepts

Amplitude

Amplitude is the magnitude of the peak (or valley) value of a sine wave, calculated as the absolute value of the coefficient in front of the sine function. It represents the maximum deviation of the function from its midline, indicating how 'tall' or 'short' the waves are.

Period

The period of a sinusoidal function is the length of one complete cycle along the x-axis. It is determined by the coefficient of x inside the sine function, with the period calculated as 2? divided by the absolute value of that coefficient. This tells you how far along the x-axis the function repeats its pattern.

Phase Shift

The phase shift is the horizontal displacement of the sine wave from its standard position. It is found by setting the inside of the sine function equal to zero and solving for x, revealing how far and in which direction (left or right) the graph is shifted from the origin.

Graphing Sinusoidal Functions

Graphing a sinusoidal function involves plotting one complete cycle of the wave based on its amplitude, period, and phase shift. This requires identifying key points such as the beginning, maximum, midpoint, minimum, and the end of the cycle, allowing for an accurate and complete visualization of the wave's behavior.

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