Answer:
Explanation:
From the given graph, we can see that the sinusoidal function has been shifted horizontally and vertically.
To find the formulas for the shifted sinusoidal function if it was originally a regular sine and cosine function, we need to consider the following:
1. Horizontal shift (phase shift): The horizontal shift is given by the value of "Aft" on the x-axis. If the graph is shifted to the right (positive value), the phase shift will be to the left by the same amount. If the graph is shifted to the left (negative value), the phase shift will be to the right by the same amount.
2. Vertical shift: The vertical shift is given by the value of "r" on the y-axis. If the graph is shifted upward (positive value), the vertical shift will be upward by the same amount. If the graph is shifted downward (negative value), the vertical shift will be downward by the same amount.
Given these considerations, the formulas for the shifted sinusoidal function if it was originally a regular sine and cosine function would be:
1. As a shifted cosine function: y = r + A * cos(B(x - Aft))
- The amplitude (A) would remain the same as the original cosine function.
- The frequency (B) would remain the same as the original cosine function.
- The phase shift (Aft) would be the opposite sign of the value shown on the x-axis.
2. As a shifted sine function: y = r + A * sin(B(x - Aft))
- The amplitude (A) would remain the same as the original sine function.
- The frequency (B) would remain the same as the original sine function.
- The phase shift (Aft) would be the opposite sign of the value shown on the x-axis.
It's important to note that without specific values provided for the horizontal shift (Aft) and vertical shift (r) on the graph, we cannot determine the exact formulas for the shifted sine and cosine functions. However, the general formulas provided above would apply once the values of Aft and r are known.