Determine the amplitude, period, and phase shift of y=2 sin(2 x-(π)/(2)) . Then graph one period

step 1 So we're being asked the graph this trig function, and the amplitude is 2. That comes from right

Determine the amplitude, period, and phase shift of y=2...

Key Concepts

Graphing Trigonometric Functions

Graphing trigonometric functions involves plotting one full cycle of the function by identifying key features such as amplitude, period, and phase shift. It requires marking critical points on the x-axis and matching them with the corresponding y-values while taking into account any transformations. Understanding these graph transformations allows for accurately depicting the behavior of the sine or cosine wave.

Phase Shift

Phase shift refers to the horizontal translation of the trigonometric function along the x-axis. It determines where the graph starts its cycle relative to the standard position. This shift is calculated by setting the inside expression of the sine or cosine function equal to zero and solving for the variable, effectively indicating how much the graph is moved left or right.

Amplitude

Amplitude is a measure of the vertical distance between the midline of a trigonometric function and its maximum (or minimum) value. It is determined by taking the absolute value of the coefficient in front of the sine or cosine function. In the context of transformed sine or cosine functions, amplitude indicates how 'tall' or 'short' the peaks and troughs of the graph will be.

Period

The period of a trigonometric function is the horizontal length of one complete cycle of the wave. It is calculated by dividing the standard period (usually 2? for sine and cosine) by the absolute value of the coefficient that multiplies the variable inside the function. This concept helps determine how frequently the function repeats its pattern over the x-axis.

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