Graph this trigonometric function. y=-4cos(x/2+3.14)+1
type into google "coolmath graphing calculator" then on the calculator, just type in -4 cos(x/2 + 3.14) + 1 and then press enter on your keyboard. the graph should show up.
To graph the trigonometric function y = -4cos(x/2+3.14)+1, we need to understand the properties and behavior of cosine function.
The general form of a cosine function is y = A*cos(B(x - C)) + D, where A represents the amplitude, B represents the horizontal stretch or compression, C represents the phase shift, and D represents the vertical shift.
In this function, y = -4cos(x/2+3.14)+1, we can identify the values of A, B, C, and D:
A = -4, which represents the amplitude. Amplitude determines the maximum vertical distance the graph reaches from its average (midpoint) value. In this case, the graph will oscillate between the values D - A and D + A.
B = 1/2, which represents the horizontal stretch or compression. A value of B less than 1 compresses the graph horizontally, and a value greater than 1 stretches it. In this case, B = 1/2, so the graph will be compressed horizontally compared to the standard cosine function.
C = 3.14, which represents the phase shift or horizontal translation. A positive value of C shifts the graph to the left, while a negative value shifts it to the right. Here, C = 3.14, indicating that the graph will shift 3.14 units to the left.
D = 1, which represents the vertical shift, moving the entire graph up or down. In this case, D = 1, so the graph will be shifted upward by one unit.
Using these values, we can understand how to draw the graph of the function. Here's how you can proceed to graph it:
1. Start by plotting the standard cosine function, y = cos(x), by picking several points and connecting them smoothly. Since the amplitude is -4, the graph will oscillate between the values 1 - 4 and 1 + 4, which are -3 and 5, respectively. So, draw a dashed line between these two horizontal lines.
2. Next, take the graph of the standard cosine and perform the horizontal stretch or compression. Since B = 1/2, multiply the x-coordinates of your points by 2. This will compress the graph horizontally.
3. After compressing the graph, shift it horizontally by C units. Here, C = 3.14, so move each of your points 3.14 units to the left.
4. Finally, shift the entire graph vertically by D units. In this case, D = 1, so move the graph upward by one unit.
5. Connect the points smoothly, following the overall shape of the transformed function.
By following these steps, you will obtain the graph of the trigonometric function y = -4cos(x/2+3.14)+1.