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

This Question is Closed

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

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

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1If 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.

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

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

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1There 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...

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

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

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

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

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1It 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...

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

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

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

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

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Identities 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!
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