Graph each function over a one-period interval. See Example 3 . y=-(1)/(2) cos4(x+(π)/(2))

Name: Problem 38, Chapter 6: Precalculus
Uploaded: 2021-06-19T15:14:27-08:00
Duration: 2 min 23 s
Channel: Abdul Vahid M
Description: Graph each function over a one-period interval. See Example 3 . y=-(1)/(2) cos4(x+(π)/(2))

step 1 Hello hi here in this question we need to draw the graph of y is equal to minus 1 by 2 cos 4 tim

Graph each function over a one-period interval. See Example...

Key Concepts

Amplitude

Amplitude is a measure of the vertical stretch or compression of a trigonometric function. It is determined by the absolute value of the coefficient in front of the cosine or sine function. In general, for a function given by y = A cos(Bx + C) or y = A sin(Bx + C), the amplitude is |A|. This concept helps in determining the peak and trough values of the graph.

Period

The period of a trigonometric function is the length of one complete cycle of the graph. For functions of the form y = cos(Bx + C) or y = sin(Bx + C), the period is calculated as 2?/|B|. Understanding the period is essential when graphing the function over one complete cycle.

Phase Shift

The phase shift of a trigonometric function represents its horizontal translation. It refers to the amount by which the base graph of the function is shifted left or right. For an equation in the form y = cos(B(x - h)), the phase shift is h, which is determined by rewriting the inside expression as Bx - Bh. Recognizing the phase shift helps in accurately placing key points of the graph on the horizontal axis.

Vertical Reflection

Vertical reflection occurs when the function is multiplied by a negative constant, which reflects the graph over the horizontal axis. For a function y = -f(x), every y-value from the original function is negated, flipping highs and lows. This concept is important to note when sketching the graph, as it affects the position of maximum and minimum values.

Graphing Trigonometric Functions

Graphing trigonometric functions involves applying several transformation concepts including amplitude, period, phase shift, and vertical reflection. By determining these parameters, one can accurately sketch the graph over one period, mark key points, and understand the behavior of the function as it repeats its cycle.

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