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anonymous
 4 years ago
Set 2*sin(x) + 3*cos(x) = C*cos(x+d). Expand the righthand side and solve for C and d.
anonymous
 4 years ago
Set 2*sin(x) + 3*cos(x) = C*cos(x+d). Expand the righthand side and solve for C and d.

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myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sin(d)\sin(x)+\cos(d)\cos(x)=\cos(xd)\] dw:1328404418705:dw

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2we want sin(d)=2 and cos(d)=3 so we have dw:1328404462699:dw

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2dw:1328404476610:dw

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\frac{\sqrt{3^2+2^2}}{\sqrt{3^2+2^2}}(2 \sin(x)+3 \cos(x))\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{3^2+2^2}( \frac{2}{\sqrt{3^2+2^2}} \sin(x)+\frac{3}{\sqrt{3^2+2^2}} \cos(x))\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{3^2+2^2}(\sin(d)\sin(x)+\cos(d)\cos(x))\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{3^2+2^2}(\cos(d)\cos(x)+\sin(d)\sin(x))=\sqrt{9+4}\cos(xd)\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{13}\cos(xd)\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2you can solve for d by solving \[\sin(d)=\frac{2}{\sqrt{13}}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{13}\cos(x\sin^{1}(\frac{2}{\sqrt{13}}))\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I am more than a little lost with what you did. I can show the answer my friend helped me with. she got it correct and I still dont get it. :(

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.2which part do you not like?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Cos (x+d) = cos(d) –sin (x) sin(d) 2 *sin (x) + 3* soc(x) = C *(cos(x) cos(d) –sin(d) 3 = C cos(d) 2= ¯ C(sin(d) C= 3/cos〖(d)〗 C = (¯2)/(sin(d)) Sin(d) (3/(cos(d))) = ((¯2)/(sin(6))) sin(d) (3 sin〖(d)〗)/cos(d) /3 = ¯2/3 (sin(d))/(cos(d))= ¯2/3 tan (d) = ¯2/3 d≈¯0.588 C = 3/(cos(d)) C= 3/(cos(¯0.588)) C≈3.6055 x y ¯5 2.7688 ¯4 ¯0.4473 ¯3 ¯3.252 ¯2 ¯3.067 ¯1 ¯0.062 0 3 1 3.3068 2 0.57015 3 ¯2.388 4 ¯3.475 5 ¯1.067

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I dont understand the first part you did. I get the graphs, but the SQRT 3^2 + 2^2/3^2 + 2^2 = 2sinx+3cosX

phi
 4 years ago
Best ResponseYou've already chosen the best response.1Start with 2*sin(x) + 3*cos(x) = C*cos(x+d) the wellknow expansion: cos(a+b)= cos(a)cos(b)sin(a)sin(b) using it in your problem: 2 sin(x) + 3 cos(x)= Ccos(d)cos(x)  C sin(d)sin(x) match corresponding terms: 2 = C sin(d) 3 = C cos(d) divide these two equations to get tan(d) = 2/3 d= 0.588 rads solve for C using either of the 2 equations. example C= 3/cos(d) > C= 3.6 so your friend did it correctly

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how do you come to the 2 = C sin(d) ? I just am not understandig that part

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes she did it correctly. and the teacher wants us to graph it.

phi
 4 years ago
Best ResponseYou've already chosen the best response.1would you rather see 2 sin(x) + 3 cos(x)= Ccos(d)cos(x)  C sin(d)sin(x) rewritten as 2 sin(x) + 3 cos(x)=  C sin(d)sin(x) + Ccos(d)cos(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol i dont know!!! I get the use of the sum equations. I just get really confused with the setting the thing to C*cos(x+d). and solving for C and d.

phi
 4 years ago
Best ResponseYou've already chosen the best response.1how about this 2 sin(x) = A sin(x) what is A? 2 sin(x) + 3 cos(x) = A sin(x) + B cos(x) what is A and B?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i have been a whole week on this problem and I have gone to the teacherand still didnt understand cause i got so upset

phi
 4 years ago
Best ResponseYou've already chosen the best response.1now do the same for 2 sin(x) + 3 cos(x)= (C sin(d)) sin(x) + (Ccos(d)) cos(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.02sin(d)sin(x) + 3cos(d)cos(x) ??????

phi
 4 years ago
Best ResponseYou've already chosen the best response.12 sin(x) + 3 cos(x) = A sin(x) + B cos(x) 2 sin(x) + 3 cos(x)= (C sin(d)) sin(x) + (Ccos(d)) cos(x) It is the same idea, except "A" in the 2nd equation is a little more complicated. But the same idea.

phi
 4 years ago
Best ResponseYou've already chosen the best response.1In the top equation you know A=2 and B=3 in the bottom equation you know (C sin(d)) = 2 and (Ccos(d))=3

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You are kind and patient. I have almost a hold on this. the teacher said that you set it to zero? so this is where (C sin(d)) = 2 and (Ccos(d))=3 then I solve for d? is that right?

phi
 4 years ago
Best ResponseYou've already chosen the best response.1no zeros in this problem. You must be thinking of another type problem. But to go on, yes solve for d by dividing the two equations. use the fact that sin(x)/cos(x) = tan(x)

phi
 4 years ago
Best ResponseYou've already chosen the best response.1myi's approach is a good one to understand. Here is the plot http://www.wolframalpha.com/input/?i=plot+3.6+cos%28x+0.588+%29

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0very cool!! thank you!! I will try the next problem which is setting it = ½*sin(x) – 1/5*cos(x).

phi
 4 years ago
Best ResponseYou've already chosen the best response.1I hope you found 0.5 sin(x)  0.2 cos(x) = 0.539 cos(x + 1.19)
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