Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 6 units and downward 6 units and is vertically stretched by a factor of 5 when compared to y=sin(x)
y = 5 sin (x-6) - 6
thankyou =)
To obtain the equation of a sine wave that is shifted to the right 6 units, downward 6 units, and vertically stretched by a factor of 5 when compared to the original function y = sin(x), you can follow these steps:
Step 1: Start with the equation of the original sine wave: y = sin(x).
Step 2: To shift the graph to the right 6 units, we need to replace x with (x - 6) in the equation: y = sin(x - 6).
Step 3: To shift the graph downward 6 units, replace y with (y - 6) in the equation: y - 6 = sin(x - 6).
Step 4: To vertically stretch the graph by a factor of 5, multiply the entire equation by 5: 5(y - 6) = 5sin(x - 6).
Therefore, the equation of the sine wave that is obtained by shifting the graph of y = sin(x) to the right 6 units, downward 6 units, and vertically stretched by a factor of 5 is 5(y - 6) = 5sin(x - 6).
To find the equation of a sine wave that is obtained by shifting the graph of y = sin(x) to the right 6 units, downward 6 units, and vertically stretched by a factor of 5, we need to make adjustments to the original equation one step at a time.
1. Shifting to the right by 6 units: To shift the graph of y = sin(x) to the right by 6 units, we replace the x in the equation with (x - 6). This adjustment moves the entire graph to the right by 6 units.
Equations becomes: y = sin(x - 6)
2. Shifting downward by 6 units: To shift the graph downward by 6 units, we subtract 6 from the equation. This adjustment moves the entire graph downward by 6 units.
Equation becomes: y = sin(x - 6) - 6
3. Vertically stretching by a factor of 5: To vertically stretch the graph by a factor of 5, we multiply the entire equation by 5. This adjustment elongates the y-values of the graph.
Equation becomes: y = 5(sin(x - 6) - 6)
Therefore, the equation of the desired sine wave is y = 5(sin(x - 6) - 6).