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anonymous
 one year ago
Will METAL!!
Verify the identity.
cos (x  y)  cos (x + y) = 2 sin x sin y
anonymous
 one year ago
Will METAL!! Verify the identity. cos (x  y)  cos (x + y) = 2 sin x sin y

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Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1we'll be using two rules here: cos(A+B) = cosA*cosB  sinA*sinB cos(AB) = cos(A)*cos(B) + sin(A)*sin(B)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1cos(xy) = cosx*cosy + sinx*siny cos(x+y) = cosx*cosy  sinx*siny therefore: cos(xy)  cos(x+y) = cosx*cosy + sinx*siny  (cosx*cosy  sinx*siny) = 2sinx*siny let me know if anything needs to be clarified

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait could you break that down a bit.

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1sure. start with cos (x  y) = cosx*cosy + sinx*siny is that clear?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1cos (x + y) = cosx*cosy  sinx*siny is that clear?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1good, now we just subtract cos(xy)  cos(x+y) = cosx*cosy + sinx*siny  (cosx*cosy  sinx*siny) is this part clear?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0alright what's next after that?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1just basic algebra after that

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1notice how the cosines cancel out

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443824395082:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443824403678:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh 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
 one year ago
Best ResponseYou've already chosen the best response.1@freckles having a bit of a brain fart about complex zeros

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol ok thats fine. one min brb

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1I remember that complex zeros come in pairs, so if 2i is a zero, then +2i must also be a zero

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1so, 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)(x2i) = 0 x^2  (2i)^2 = x^2  (4) = x^2 + 4 as our polynomial

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1then 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443824947058:dw (it's been so long since I've done this lol)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443825019233:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443825082485:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1that leaves us with x^2  25 and the roots of that polynomial are 5 and 5

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1anyway, that means our missing roots are 5 and 5, would you like me to go over anything with you?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1hopefully I didnt make a mistake somewhere

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Vocaloid sorry I lost connection.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For 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
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443825614299:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1hint: to find the vertical asymptote, set the denominator equal to 0
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