Question

Find the equation of a sine wave that is obtained by shifting the graph of y = sin(x) to the right 7 units and downward 8 units and is vertically stretched by a factor of 2 when compared to y = sin(x). y =

Answer 1

The equation of the shifted and stretched sine wave is y = 2 * sin(x - 7) - 8.

Step-by-step explanation:

The equation of the shifted and stretched sine wave is y = 2 * sin(x - 7) - 8.

The original equation for a sine wave is y = sin(x), where x is the angle and y is the value of the wave at that angle. To shift the graph to the right by 7 units, we subtract 7 from x in the equation, resulting in y = sin(x - 7). To shift the graph downward by 8 units, we subtract 8 from the entire equation, resulting in y = sin(x - 7) - 8.

To vertically stretch the graph by a factor of 2, we multiply the entire equation by 2, resulting in y = 2 * sin(x - 7) - 8.

Answer 2

To shift the graph of y = sin(x) to the right 7 units and downward 8 units and vertically stretched by a factor of 2, the equation of the sine wave is y = 2 × sin(x - 7) - 8.

Step-by-step explanation:

To find the equation of a sine wave obtained by shifting the graph of y = sin(x), we need to consider three transformations: a horizontal shift of 7 units to the right, a vertical shift of 8 units downward, and a vertical stretch by a factor of 2.

First, let's start with the original equation y = sin(x). To shift it 7 units to the right, we replace x with (x - 7), giving us y = sin(x - 7). Then, to shift it 8 units downward, we subtract 8 from the equation, resulting in y = sin(x - 7) - 8.

Finally, to vertically stretch it by a factor of 2, we multiply the equation by 2, giving us y = 2 × sin(x - 7) - 8.

Therefore, the equation of the sine wave is y = 2 × sin(x - 7) - 8.