The amplitude of a trigonometric function is the absolute value of the coefficient of the sine or cosine function. In this case, the amplitude is |−6| = 6.

The period of a sine or cosine function is given by 2π divided by the absolute value of the coefficient of x inside the sine or cosine function. In this case, the period is 2π / |5| = 2π/5.

To sketch the graph, you would start by drawing a horizontal line (the x-axis) and marking off a distance along the x-axis that represents one period of the function. Then, you would draw a vertical line (the y-axis) through the midpoint of this interval.

The graph of the function will be a wave that oscillates between -6 and 6 on the y-axis, with a period of 2π/5. Because the coefficient of the sine function is negative, the graph will be a reflection of the usual sine curve across the x-axis.

Finally, the "+6" at the end of the function indicates a vertical shift upwards by 6 units. So, you would shift the entire graph upwards by 6 units.

Please note that I can't actually draw the graph here, but I hope these instructions help you to draw it in your notebook.

Question

The amplitude of a trigonometric function is the absolute value of the coefficient of the sine or cosine function. In this case, the amplitude is |−6| = 6.

The period of a sine or cosine function is given by 2π divided by the absolute value of the coefficient of x inside the sine or cosine function. In this case, the period is 2π / |5| = 2π/5.

To sketch the graph, you would start by drawing a horizontal line (the x-axis) and marking off a distance along the x-axis that represents one period of the function. Then, you would draw a vertical line (the y-axis) through the midpoint of this interval.

The graph of the function will be a wave that oscillates between -6 and 6 on the y-axis, with a period of 2π/5. Because the coefficient of the sine function is negative, the graph will be a reflection of the usual sine curve across the x-axis.

Finally, the "+6" at the end of the function indicates a vertical shift upwards by 6 units. So, you would shift the entire graph upwards by 6 units.

Please note that I can't actually draw the graph here, but I hope these instructions help you to draw it in your notebook.

Knowee AI · Accepted Answer

The amplitude of a trigonometric function is the absolute value of the coefficient of the sine or cosine function. In this case, the amplitude is |−6| = 6.

The period of a sine or cosine function is given by 2π divided by the absolute value of the coefficient of x inside the sine or cosine function. In this case, the period is 2π / |5| = 2π/5.

To sketch the graph, you would start by drawing a horizontal line (the x-axis) and marking off a distance along the x-axis that represents one period of the function. Then, you would draw a vertical line (the y-axis) through the midpoint of this interval.

The graph of the function will be a wave that oscillates between -6 and 6 on the y-axis, with a period of 2π/5. Because the coefficient of the sine function is negative, the graph will be a reflection of the usual sine curve across the x-axis.

Finally, the "+6" at the end of the function indicates a vertical shift upwards by 6 units. So, you would shift the entire graph upwards by 6 units.

Please note that I can't actually draw the graph here, but I hope these instructions help you to draw it in your notebook.

Find the amplitude and period of the following trigonometric function. Sketch the graph in your notebook.𝑓(𝑥)=−6sin(5𝑥)+6

Question

Find the amplitude and period of the following trigonometric function.

Solution

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