A sine function has the following key features:
Frequency = 14π
Amplitude = 2
Midline: y = 2
y-intercept: (0, 2)
how would i graph this?
To graph a sine function with the given key features, you will follow these steps:
1. Determine the period: The period of a sine function is the distance between two consecutive peaks or troughs. In this case, the given frequency is 14π, so the period is found by dividing 2π by the frequency: Period = 2π / (14π) = 1 / 7.
2. Determine the amplitude: The amplitude of a sine function is the distance from the midline (average value) to the peak or trough. The given amplitude is 2 units.
3. Determine the midline: The midline is the line that the sine function oscillates around. In this case, the given midline is y = 2.
4. Determine the phase shift: The phase shift represents how the graph is shifted horizontally. In this case, there is no specified phase shift, so it is assumed to be 0.
5. Plot the key points: Start by locating the y-intercept at (0, 2). Then, calculate the coordinates of a few more key points using the formula:
x = (2π / Period) * (angle in degrees) + phase shift
y = amplitude * sin(x) + midline
For example, to find the first peak, plug in an angle of 90 degrees:
x = (2π / (1/7)) * 90 + 0 = 2π * (7/90)
y = 2 * sin(2π * (7/90)) + 2
Calculate a few more points in a similar manner to get a good representation of the graph.
6. Sketch the graph: Once you have plotted several key points, connect them smoothly to form a continuous curve. Make sure to maintain the period and amplitude as you draw the graph.
By following these steps, you will be able to graph the given sine function with the provided key features.
y = a sin (2 pi f - p) + b
y = 2 sin (2 pi f - p) + 2
I doubt if you mean f = 14 pi
I bet you mean omega = 2 pi f = 14 pi
then
y = 2 sin (14 pi t - p) + 2
hen t = 0, y = 2
that works for p = 0 (the phase)
so
y = 2 sin (14 pi t) + 2
I used t, you can use x if you wish.