The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.
First graph;
a. Amplitude = 0.5
b. The period = 2•π
c. The horizontal shift = 1
d. The vertical shift = π/4
Second graph;
a. Amplitude = 2
b. The period = π
c. The horizontal shift = -π/4
d. The vertical shift = -2
Which method can be used to find the graph parameters?
First graph;
a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.
The coordinate of a peak point in the first graph is (0, -1.5)
The coordinate of a throw point is (π/2, -2.5)
Therefore;
Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5
b. The period is the number of cycles per second, we have;
- Period = 1/f
- f = Frequency
From the graph, we have;
Therefore;
The frequency = 1/π cycle per unit length
c. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.
Therefore;
The horizontal shift = (-π/2)/2 = -π/4
d. The vertical shift is the distance from the horizontal axis to the midline of the graph.
By observation, the midline is y = -2
Therefore;
Second Graph;
For the second graph, we have;
a. Amplitude = (3 - (-1))/2 = 2
b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)
Therefore;
- Period = 1/(1/(2•π)) = 2•π
c. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.
Therefore;
- Horizontal shift = π/4 - 0 = π/4
d. Vertical shift = (3 + (-1))/2 = 1
Learn more about the graphs of sinusoidal functions here:
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