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jahvoan
Group Title
Solve each equation for 0 = x = 2π :
i) 2cos^(2)x + 3cosx – 2 = 0
ii) sinx = sqrt 3cosx
(Rewards for correct answer)
 one year ago
 one year ago
jahvoan Group Title
Solve each equation for 0 = x = 2π : i) 2cos^(2)x + 3cosx – 2 = 0 ii) sinx = sqrt 3cosx (Rewards for correct answer)
 one year ago
 one year ago

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enka Group TitleBest ResponseYou've already chosen the best response.0
did you mean \[ (1)\quad2cos^2x+3cosx−2=0\\ (2)\quad \sin x=\sqrt{3}\cos x\\ \text{for }0\le x \le2\pi\] ???
 one year ago

darkb0nebeauty Group TitleBest ResponseYou've already chosen the best response.0
a. (2cosx1)(cosx+2)=0 cosx=1/2 or cosx=2 x={π/3, 5π/6} This is correct, i promise...
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
If you set p=cos x in the first one, you get: 2p²+3p2=0. You can solve this, using the quadratic formula. Once you've got you p, remember cos x = p, so solve for x.
 one year ago

darkb0nebeauty Group TitleBest ResponseYou've already chosen the best response.0
Do you get mines @jahvoan
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
i got the answer but what is the corresponding angle for 2 on the unit circle?
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
There isn't. cosx=2 has no solutions, because the xcoordinate of a point on the unit circle (which is the cosine) only has values from 1 to 1...
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
solve equation 2
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
You can divide both sides by cos x and remember sinx/cosx = tan x
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
but on the right it is sqrt cosx
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
No, it's sqrt(3) * cosx
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
no look at the problem up top
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
It says: sinx = sqrt 3cosx This can only mean:\[ \sin x = \sqrt{3} \cdot \cos x\]So dividing by cos x gives:\[\frac{ \sin x }{\cos x }=\sqrt{3} \Leftrightarrow \tan x=\sqrt{3}\]And this is a "nice" value of tan x. If you interpret it otherwise, you can't solve it...
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
so what will be the answer for sqrt 3 on the unit circle?
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
Remember that special triangle with sides of a, 2a and a√3?
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
is it pi/6
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
no its pi/3 right or wrong?
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
60 degrees, or pi/3
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
thanks mayne
 one year ago

jahvoan Group TitleBest ResponseYou've already chosen the best response.0
why is equation 2 not considered to be an identity?
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
Identities hold for every x. This one is only true if x = pi/3. Identity: sinx=cos(pi/2x). No matter what x is, it's always true!
 one year ago
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