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BloomLocke367

  • one year ago

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  1. BloomLocke367
    • one year ago
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    What values for \(\Large\theta(0\le\theta\le2\pi)\) satisfy the equation? \(\Large2\sin\theta\cos\theta+\sqrt3\cos\theta=0\)

  2. geerky42
    • one year ago
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    Factor \(\cos\theta\) out; \(\Large\cos\theta(2\sin\theta+\sqrt3)=0\) Then now we can split into two equations; \(\cos\theta = 0\) OR \(2\sin\theta+\sqrt3=0\) Right?

  3. BloomLocke367
    • one year ago
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    I guess so? I don't remember how I started working on this earlier, but I already have 2 answers, but there are 2 more

  4. geerky42
    • one year ago
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    WWhat answer do you have?

  5. geerky42
    • one year ago
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    \(\dfrac{\pi}{2}\) and \(\dfrac{3\pi}{2}\), right?

  6. BloomLocke367
    • one year ago
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    pi/2 and 3pi/2. I used the unit circle to find the values for when cos=0

  7. BloomLocke367
    • one year ago
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    yes

  8. geerky42
    • one year ago
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    ok. now we solve for \(2\sin\theta+\sqrt3 = 0\) Try isolate \(\sin\theta\).

  9. geerky42
    • one year ago
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    Then use unit circle

  10. BloomLocke367
    • one year ago
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    ohhh \(\sin\theta=-\sqrt3/2\) so the answers are \(\Large\frac{5\pi}{6}\) and \(\Large\frac{7\pi}{6}\)

  11. BloomLocke367
    • one year ago
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    right?

  12. BloomLocke367
    • one year ago
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    wait... I used cos, not sin

  13. BloomLocke367
    • one year ago
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    the answers are \(\Large\frac{4\pi}{3}\) and \(\Large\frac{5\pi}{3}

  14. BloomLocke367
    • one year ago
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    oops

  15. geerky42
    • one year ago
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    Right.

  16. BloomLocke367
    • one year ago
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    \(\Large\frac{5\pi}{3}\)

  17. BloomLocke367
    • one year ago
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    thank you!! some more?

  18. geerky42
    • one year ago
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    sure

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