anonymous
  • anonymous
Will METAL!! Verify the identity. cos (x - y) - cos (x + y) = 2 sin x sin y
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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Vocaloid
  • Vocaloid
we'll be using two rules here: cos(A+B) = cosA*cosB - sinA*sinB cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B)
Vocaloid
  • Vocaloid
cos(x-y) = cosx*cosy + sinx*siny cos(x+y) = cosx*cosy - sinx*siny therefore: cos(x-y) - cos(x+y) = cosx*cosy + sinx*siny - (cosx*cosy - sinx*siny) = 2sinx*siny let me know if anything needs to be clarified
anonymous
  • anonymous
wait could you break that down a bit.

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Vocaloid
  • Vocaloid
sure. start with cos (x - y) = cosx*cosy + sinx*siny is that clear?
anonymous
  • anonymous
yes
Vocaloid
  • Vocaloid
cos (x + y) = cosx*cosy - sinx*siny is that clear?
anonymous
  • anonymous
yes
Vocaloid
  • Vocaloid
good, now we just subtract cos(x-y) - cos(x+y) = cosx*cosy + sinx*siny - (cosx*cosy - sinx*siny) is this part clear?
anonymous
  • anonymous
alright what's next after that?
Vocaloid
  • Vocaloid
just basic algebra after that
Vocaloid
  • Vocaloid
notice how the cosines cancel out
Vocaloid
  • Vocaloid
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Vocaloid
  • Vocaloid
|dw:1443824403678:dw|
anonymous
  • anonymous
oh ok, could we do. Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x4 - 21x2 - 100
Vocaloid
  • Vocaloid
@freckles having a bit of a brain fart about complex zeros
anonymous
  • anonymous
lol ok thats fine. one min brb
Vocaloid
  • Vocaloid
I remember that complex zeros come in pairs, so if -2i is a zero, then +2i must also be a zero
Vocaloid
  • Vocaloid
so, we can write an expression using each root x + 2i = 0 x - 2i = 0 then I'm guessing we multiply these two together to get (x+2i)(x-2i) = 0 x^2 - (2i)^2 = x^2 - (-4) = x^2 + 4 as our polynomial
Vocaloid
  • Vocaloid
then we take our original function f(x) = x4 - 21x2 - 100 divide by the polynomial we just got x^2 + 4 using synthetic division, I presume
Vocaloid
  • Vocaloid
|dw:1443824947058:dw| (it's been so long since I've done this lol)
Vocaloid
  • Vocaloid
|dw:1443825019233:dw|
Vocaloid
  • Vocaloid
|dw:1443825082485:dw|
Vocaloid
  • Vocaloid
that leaves us with x^2 - 25 and the roots of that polynomial are 5 and -5
Vocaloid
  • Vocaloid
anyway, that means our missing roots are 5 and -5, would you like me to go over anything with you?
Vocaloid
  • Vocaloid
hopefully I didnt make a mistake somewhere
anonymous
  • anonymous
@Vocaloid sorry I lost connection.
anonymous
  • anonymous
For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine x = 3, x = -3, y = 1 x = 9, y = 3 None x = 9, y = 1
anonymous
  • anonymous
options^
anonymous
  • anonymous
|dw:1443825614299:dw|
Vocaloid
  • Vocaloid
hint: to find the vertical asymptote, set the denominator equal to 0

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