DominiRican1013
  • DominiRican1013
If cos(x)cos(pi/7)+sin(x)sin(pi/7)=-V2/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
1. ∫ cos³(πx) dx 2. ∫ cos²(πx) cos(πx) dx 3. ∫(1 - sin²(πx)) cos(πx) dx 4. ∫ cos(πx) dx - ∫ sin²(πx) cos(πx) dx Set u=πx, du=π dx Set v=sin(u), dv=cos(u) du 5. 1 ⁄ π ∫ cos(u) du - 1 ⁄ π ∫ v² dv 6. 1 ⁄ π [ ∫ cos(u) du - ∫ v² dv ] 7. 1 ⁄ π [ sin(u) - v³ ⁄ 3 ] + C 8. 1 ⁄ π [ sin(πx) - sin³(πx) ⁄ 3 ] + C 9. sin(πx) ⁄ π - sin³(πx) ⁄ (3π) + C One day you will know Euler's as the most versatile tidbit of knowledge on the planet. 10. ∫ cos³(πx) dx 11. ∫ [(e^(iπx) + e^(-iπx)) ⁄ 2]³ dx 12. ⅛ ∫ [e^(iπx) + e^(-iπx)]³ dx 13. ⅛ ∫ [e^(3iπx) + e^(-3iπx) + 3e^(iπx) + 3e^(-iπx)] dx 14. ⅛ [∫ e^(3iπx) dx + ∫ e^(-3iπx) dx + 3∫ e^(iπx) dx + 3∫ e^(-iπx) dx] 15. ⅛ [e^(3iπx) ⁄ (3iπ) + e^(-3iπx) ⁄ (-3iπ) + 3e^(iπx) ⁄ (iπ) + 3e^(-iπx) ⁄ (-iπ)] + C 16. ⅛ [(1 ⁄ (3iπ))(e^(3iπx) - e^(-3iπx)) + (3 ⁄ (iπ))(e^(iπx) - e^(-iπx))] + C 17. ⅛ [(1 ⁄ (3iπ))(2i sin(3πx)) + (3 ⁄ (iπ))(2i sin(πx))] + C 18. ⅛ [(2 sin(3πx)) ⁄ (3π) + (6 sin(πx)) ⁄ π] + C 19. [sin(3πx) + 9 sin(πx)] ⁄ (12π) + C Which is another way of saying the same thing. Pick your poison. But note the link below. Wolfram's alpha sets it up with Euler's.
DominiRican1013
  • DominiRican1013
If \[\cos(x)\cos(\frac{ \pi }{ 7 })+\sin(x)\sin(\frac{ \pi }{ 7 })=-{\frac{ \sqrt{2} }{ 2 }}\] then x can equal:(check all that apply)
anonymous
  • anonymous
Does that help?

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welshfella
  • welshfella
LHS = cos (x - pi/7)
welshfella
  • welshfella
cos (x - pi/7) = -sqrt2/2
DominiRican1013
  • DominiRican1013
Woud you like me to put the choices?
welshfella
  • welshfella
ang;es whose cosine is -sqrt2/2 = 3pi/4 and 5pi/4 ( in the range 0 to 2pi)
LynFran
  • LynFran
|dw:1437059667158:dw|
welshfella
  • welshfella
x - pi7 = 3pi/4 and x - pi/7 = 5pi/4 solve for x
DominiRican1013
  • DominiRican1013
\[A. 7\pi/4+\pi/7+2npi\]
DominiRican1013
  • DominiRican1013
\[B. 5\pi/4+\pi/7+2npi\]
DominiRican1013
  • DominiRican1013
\[C. \pi/4+\pi/7+2npi\]
DominiRican1013
  • DominiRican1013
\[D. 3\pi/4+\pi/7+2npi\]
welshfella
  • welshfella
the 2n pi means that the solutions contain an infinite number of higher angles - you should be able to find the correct options from my last post
welshfella
  • welshfella
x - pi7 = 3pi/4 add pi/7 to both sides x = 3pi/4 + pi/7
welshfella
  • welshfella
oh add the 2npi!
LynFran
  • LynFran
the cos function |dw:1437060458196:dw|
LynFran
  • LynFran
what is your principal value here?
DominiRican1013
  • DominiRican1013
pi/7?
LynFran
  • LynFran
no..|dw:1437060724407:dw|
DominiRican1013
  • DominiRican1013
C and D?
LynFran
  • LynFran
|dw:1437060913877:dw|
welshfella
  • welshfella
I've done one of them for you in my last post
DominiRican1013
  • DominiRican1013
I got that one.... do any of the others apply because the problem asks for check all that apply
DominiRican1013
  • DominiRican1013
except from D
LynFran
  • LynFran
yes check here .. https://www.symbolab.com/solver/trigonometric-equation-calculator/cos%5Cleft(x-%5Cfrac%7B%5Cpi%7D%7B7%7D%5Cright)%3D%5Cfrac%7B-%5Csqrt%7B2%7D%7D%7B2%7D/?origin=enterkey
LynFran
  • LynFran
so what the other option ?
DominiRican1013
  • DominiRican1013
it was B and D not C :)
LynFran
  • LynFran
correct

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