Question 1125441: The graph of y = psinax have a amplitude of 3 and a period of 180°.if the one turning point is (135°;-3),Then the value of a=? And p=?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formula for the sine wave is shown in the following link.
https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html
the formula shown in the link is y = A * sin(B * (x - C) ) + D
A is the amplitude.
B is the frequency.
C is the horizontal shift.
D is the vertical shift.
in your problem, what they call A, you call p, and what they call B, you call a.
the amplitude is 3, therefore p = 3.
the period is 180 degrees.
this means that the number of degrees for the sine wave to make one complete cycle is 180 degrees.
the formula for period is p = 360 / f, and the formula for frequency is f = 360 / p.
you are given that the period is 180 degrees.
to find the frequency, use the formula for f = 360 / p.
that becomes f = 360 / 180 = 2.
the frequency is 2, which is the value of the variable a in your problem (called B in the reference).
your formula then becomes y = 3 * sin(2 * x).
here's the graph.
from the graph, you can see thqt the turning point is at (135 degrees, -3).
the period is 180 degrees and the amplitude is 3.
an amplitude of 3 means the graph goes plus or minus 3 units from the denter line.
the center line of this graph is at y = 0.
the blue line is the graph.
the orange line is used so that i can show the intersection of the graph with the value of x = 135 degrees.
the orange shading is used to frame the 180 degree cycle of the sine wave.
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