anonymous
  • anonymous
Solve each equation for 0 = x = 2π : i) 2cos^(2)x + 3cosx – 2 = 0 ii) sinx = sqrt 3cosx (Rewards for correct answer)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
did you mean \[ (1)\quad2cos^2x+3cosx−2=0\\ (2)\quad \sin x=\sqrt{3}\cos x\\ \text{for }0\le x \le2\pi\] ???
anonymous
  • anonymous
a. (2cosx-1)(cosx+2)=0 cosx=1/2 or cosx=-2 x={π/3, 5π/6} This is correct, i promise...
ZeHanz
  • ZeHanz
If you set p=cos x in the first one, you get: 2p²+3p-2=0. You can solve this, using the quadratic formula. Once you've got you p, remember cos x = p, so solve for x.

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anonymous
  • anonymous
Do you get mines @jahvoan
anonymous
  • anonymous
i got the answer but what is the corresponding angle for -2 on the unit circle?
ZeHanz
  • ZeHanz
There isn't. cosx=-2 has no solutions, because the x-coordinate of a point on the unit circle (which is the cosine) only has values from -1 to 1...
anonymous
  • anonymous
ok thanks
anonymous
  • anonymous
solve equation 2
ZeHanz
  • ZeHanz
You can divide both sides by cos x and remember sinx/cosx = tan x
anonymous
  • anonymous
but on the right it is sqrt cosx
ZeHanz
  • ZeHanz
No, it's sqrt(3) * cosx
anonymous
  • anonymous
no look at the problem up top
ZeHanz
  • ZeHanz
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...
anonymous
  • anonymous
so what will be the answer for sqrt 3 on the unit circle?
ZeHanz
  • ZeHanz
Remember that special triangle with sides of a, 2a and a√3?
anonymous
  • anonymous
is it pi/6
anonymous
  • anonymous
no its pi/3 right or wrong?
ZeHanz
  • ZeHanz
60 degrees, or pi/3
anonymous
  • anonymous
thanks mayne
anonymous
  • anonymous
why is equation 2 not considered to be an identity?
ZeHanz
  • ZeHanz
Identities hold for every x. This one is only true if x = pi/3. Identity: sinx=cos(pi/2-x). No matter what x is, it's always true!

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