What is the graph of y= 5sin1/2(x+pi)-1
the basic shape is given by
y = 5 sin (1/2)x
the amplitude of that is 5 and its period is 4π or 720°
make a sketch of that , then
shift it to the left π units and then down 1 unit
To understand the graph of the given equation, y = 5sin(1/2(x+π))-1, we can break it down into its key components and analyze them individually.
1. Amplitude (A): The amplitude of a sine function determines the maximum and minimum values of the waveform. In this case, the amplitude is 5, which means the graph will oscillate between y = 5 and y = -5.
2. Period (T): The period of a sine function defines the length of one complete cycle. The period is calculated using the formula T = 2π/b, where b is the coefficient of x inside the sine function. In this case, b = 1/2, so T = 2π/(1/2) = 4π.
3. Phase Shift (ϕ): The phase shift indicates the horizontal shift of the sine wave. It is calculated using the formula ϕ = -c/b, where c is the constant term inside the parentheses. In this case, c = π, so ϕ = -(π)/(1/2) = -2π.
4. Vertical Shift: The vertical shift is the constant added or subtracted to the entire function, shifting the graph up or down. In this case, the vertical shift is -1, which means the graph will be shifted downward by one unit.
Now, let's use this information to plot the graph:
1. Start by plotting the central points of each cycle with a distance of 4π. The first point is at ϕ = -2π, which is one complete cycle to the right.
2. Since the amplitude is 5 and the vertical shift is -1, the highest point of each cycle will be at y = 5 - 1 = 4, and the lowest point will be at y = -5 - 1 = -6. Plot these points.
3. Repeat steps 1 and 2 to plot additional points along the graph.
4. Connect the plotted points smoothly to form the graph.
Following these steps, you can now visualize and sketch the graph of y = 5sin(1/2(x+π))-1.