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secondary 4 | A Maths
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I need help with (b)
Date Posted: 4 years ago
Views: 218
Observe that the graph has a lowest y-value of 1 and a lowest y-value of 3. This denotes that the difference in the highest and the lowest value of y for the graph is 2.
The amplitude measures the distance of the graph from the centre height to either the maximum or the minimum, which is essentially half the difference mentioned above.
As such, the amplitude of the graph is 1.
In the equation, the amplitude of the graph is denoted as a. Hence, a = 1.
The centre y-value of the graph is located at y = 2. This represents the “vertical shift” of the graph from the x-axis.
In the equation, this is denoted as c. Hence, c = 2.
Now, observe that there are two complete cycles of the graph, the first being from -12pi to 0 and the second being 0 to 12pi.
This means that the period of the graph is 12pi, since a full cycle completes itself in a duration of 12pi radians.
The formula given for the frequency of the graph is f = 2pi / period. Frequency represents the number of cycles of the graph completed in a period of 2pi radians.
If 12pi radians is one full cycle for the graph, then 2pi radians is 1/6 of a full cycle for the graph.
Hence, the frequency is 1/6. In the question, it is written as (1/b) * x, so 1/b = 1/6. As such, b = 6.
The amplitude measures the distance of the graph from the centre height to either the maximum or the minimum, which is essentially half the difference mentioned above.
As such, the amplitude of the graph is 1.
In the equation, the amplitude of the graph is denoted as a. Hence, a = 1.
The centre y-value of the graph is located at y = 2. This represents the “vertical shift” of the graph from the x-axis.
In the equation, this is denoted as c. Hence, c = 2.
Now, observe that there are two complete cycles of the graph, the first being from -12pi to 0 and the second being 0 to 12pi.
This means that the period of the graph is 12pi, since a full cycle completes itself in a duration of 12pi radians.
The formula given for the frequency of the graph is f = 2pi / period. Frequency represents the number of cycles of the graph completed in a period of 2pi radians.
If 12pi radians is one full cycle for the graph, then 2pi radians is 1/6 of a full cycle for the graph.
Hence, the frequency is 1/6. In the question, it is written as (1/b) * x, so 1/b = 1/6. As such, b = 6.
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This is not the working you should use, but this is rather an explanation as to how you get the values for A B and C. Hope this helps!
Date Posted:
4 years ago
Thank you! The ans key said a=1 so i thought it was off and submitted the qn here xD
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