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secondary 4 | A Maths
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Hi! Good afternoon !
Can someone help me with all of these parts ? especially for the period and equation as i can’t tell whether it’s a sine or cosine graph ..
Thanks so much :DD
I give you a clue first: it’s a cosine graph since the graph cuts the y axis at its maximum value.
Amplitude = 2 (maximum displacement from x-axis in this case, or (highest point - lowest point) ÷ 2
Sonia, I will write this question down for you with explanations by 4 am.
y = 2cos(x/4)
or
y = 2sin(π/2 - x/4)
or
y = 2sin(x/4 + π/2)
For the last part,
k + 8π = m
Or
2cos((k+8π)/4) = 2 cos(k/4 + 2π) = 2cos(m/4)
I will analyse that graph in detail later.
I have done a cross-analysis in Desmos with the equation y = 2 cos (0.25pi x) and found that the point where y = -1.5 is when x = -3.0798.
So, in the actual graph y = 2 cos (0.25x), k should be approximately -3.0798pi.
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For this curve, at your level, you will only be required to sketch graphs of y = a sin bx + c and y = a cos bx + c, rather than y = a sin (bx + c) + d or y = a cos (bx + c) + d.
As such, for graphs starting at the centre point from the y-axis, it would be a sine curve. Specifically, we have a positive sine curve if the curve goes up first and a negative sine curve if the curve goes down first.
For graphs starting at the maximum point from the y-axis (heading downwards), it would be a positive cosine curve. For graphs starting at the minimum point from the y-axis (heading upwards), it would be a negative cosine curve.
Let me know if you need more explanation and I will do my best to explain them again!