Komposisi Translasi (Fungsi Trigonometri)

Summary

This educational video explains how to graph a trigonometric function involving both horizontal and vertical translations. The example provided is the graph of the function f(x) = 2Sin(2x - 45°) - 1 over the interval 0-360°. The process includes identifying key components such as amplitude, period, and phase shift. The steps to graph are clearly outlined: first graphing the basic function, then applying horizontal and vertical translations. Key points such as maximum and minimum values, along with the period of the function, are covered. The video emphasizes a methodical approach to plotting trigonometric graphs, with helpful tips for understanding transformations.

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Q & A

What is the main topic of the lesson in the provided transcript?

The main topic of the lesson is about sketching the graph of a trigonometric function involving both horizontal and vertical translations.

What is the given function to be graphed in the lesson?

The given function to be graphed is f(x) = 2 sin(2x - 45°) - 1 within the interval of 0 to 360 degrees.

What is the first step in graphing the given trigonometric function?

The first step is to graph the basic function y = 2 sin(2x), which serves as the starting point before applying any translations.

What does the negative value of 45° inside the function represent?

The negative 45° inside the function represents a horizontal translation to the right by 45°.

What does the '-1' in the function signify in terms of graph translation?

The '-1' in the function represents a vertical translation downward by one unit.

How do you determine the maximum and minimum values of the function y = 2 sin(2x)?

For the function y = 2 sin(2x), the maximum value is 2 and the minimum value is -2, since the amplitude is 2.

What is the period of the function y = 2 sin(2x)?

The period of the function y = 2 sin(2x) is 180° because the coefficient of 'x' (which is 2) reduces the period of the basic sine function (360°) by a factor of 2.

How do you shift the graph of y = 2 sin(2x) horizontally?

To shift the graph of y = 2 sin(2x) horizontally, we move it 45° to the right because of the negative 45° inside the sine function.

What happens after shifting the graph of y = 2 sin(2x) by 45° to the right?

After shifting the graph by 45° to the right, the x-intercepts of the graph change to 45° and 225°.

How do you account for the vertical shift in the final graph of y = 2 sin(2x - 45°) - 1?

To account for the vertical shift, you move the graph downward by one unit, so the maximum value becomes 1 and the minimum value becomes -3.