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jahvoan
 3 years ago
Solve each equation for 0 = x = 2π :
i) 2cos^(2)x + 3cosx – 2 = 0
ii) sinx = sqrt 3cosx
(Rewards for correct answer)
jahvoan
 3 years 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
 3 years 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
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Do you get mines @jahvoan

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

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

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

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

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

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

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

ZeHanz
 3 years 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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