Write the equation for the curve in its final position. The graph y=sin(x) is reflected in the x-axis, shifted a distance of pi/12 to the right, vertically stretched by a factor of 7, translated 3 units downward.
The equation for the curve in its final position can be obtained by applying each transformation one by one:
1. Reflection in the x-axis: This can be achieved by multiplying the equation by -1. So the equation becomes y = -sin(x).
2. Shift to the right by pi/12: To shift the graph to the right, we subtract pi/12 from x. The equation becomes y = -sin(x - pi/12).
3. Vertical stretching by a factor of 7: To vertically stretch the graph, we multiply the equation by 7. The equation becomes y = -7*sin(x - pi/12).
4. Translation downward by 3 units: To translate the graph downward, we subtract 3 from y. The equation becomes y = -7*sin(x - pi/12) - 3.
Therefore, the equation for the curve in its final position is y = -7*sin(x - pi/12) - 3.