please attempt all or else do not answer The following represents the graph of t
ID: 2911284 • Letter: P
Question
please attempt all or else do not answer
The following represents the graph of the function: sinxt sin3 2sin 2x f(x) = -1 Based on the graph of this function do the following: 1. Use your understanding of how to identify the parameters of the sinusoidal function y-a sin(bx+ c)+ d or y= a cosbx+ c to write the equation of a simpler function p(x) that describes the graph. Explain your choices. (W rite an equation of the graph above, explain why you choose each parameter) 2 Check the answer you obtained in (a) by graphing the new function p(x). Explain how you used your graphing calculator to verify that your answer is correct. (I do not need to see the graph but explain why this proves the identity graphically) 3. Verify algebraically that the two equations are equivalent.(You are proving an identity! Show each step.)Explanation / Answer
1)
Notice that the max is at x = 0
So, this is a perfect cos curve with no phase shift
period = distacne between two max-es or mins
And this seems like approx 2pi
So, B = 2pi/period = 2pi/2pi = 1
Amplitude :
Max = 1
Min = -1
amplitude = (max - min)/2 = (1 - (-1))/2 = 1
D :
(max + min)/2
(1 + (-1))/2
= 0
So, we have
B = 1
A = 1
D = 0
C = 0
So, it is
Acos(bx + c) + d
y = cos(x) ----> ANS
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2)
Well, i graphed both on the same graph
and they overlapped, thus same
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3)
Take (sinx + sin3x)/(2sin2x)
We know sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)
So, sinx + sin3x = 2sin(x+3x)/2cos(x-3x)/2
= 2sin(4x/2)cos(-2x/2)
= 2sin(2x)cos(-x)
but cos(-x) = cosx
So, 2sin(2x)cos(x)
Btu we had
(sinx + sin3x)/(2sin2x)
which now becomesS :
2sin(2x)cos(x) / (2sin2x)
Cancel the 2sin2x, we are left with :
cos(x)
Hence proved!
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