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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)

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  1. enka
    • 3 years ago
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    did you mean \[ (1)\quad2cos^2x+3cosx−2=0\\ (2)\quad \sin x=\sqrt{3}\cos x\\ \text{for }0\le x \le2\pi\] ???

  2. darkb0nebeauty
    • 3 years ago
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    a. (2cosx-1)(cosx+2)=0 cosx=1/2 or cosx=-2 x={π/3, 5π/6} This is correct, i promise...

  3. ZeHanz
    • 3 years ago
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    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.

  4. darkb0nebeauty
    • 3 years ago
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    Do you get mines @jahvoan

  5. jahvoan
    • 3 years ago
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    i got the answer but what is the corresponding angle for -2 on the unit circle?

  6. ZeHanz
    • 3 years ago
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    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...

  7. jahvoan
    • 3 years ago
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    ok thanks

  8. jahvoan
    • 3 years ago
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    solve equation 2

  9. ZeHanz
    • 3 years ago
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    You can divide both sides by cos x and remember sinx/cosx = tan x

  10. jahvoan
    • 3 years ago
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    but on the right it is sqrt cosx

  11. ZeHanz
    • 3 years ago
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    No, it's sqrt(3) * cosx

  12. jahvoan
    • 3 years ago
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    no look at the problem up top

  13. ZeHanz
    • 3 years ago
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    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...

  14. jahvoan
    • 3 years ago
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    so what will be the answer for sqrt 3 on the unit circle?

  15. ZeHanz
    • 3 years ago
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    Remember that special triangle with sides of a, 2a and a√3?

  16. jahvoan
    • 3 years ago
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    is it pi/6

  17. jahvoan
    • 3 years ago
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    no its pi/3 right or wrong?

  18. ZeHanz
    • 3 years ago
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    60 degrees, or pi/3

  19. jahvoan
    • 3 years ago
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    thanks mayne

  20. jahvoan
    • 3 years ago
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    why is equation 2 not considered to be an identity?

  21. ZeHanz
    • 3 years ago
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    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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