BloomLocke367
  • BloomLocke367
question below!
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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BloomLocke367
  • BloomLocke367
What values for \(\Large\theta(0\le\theta\le2\pi)\) satisfy the equation? \(\Large2\sin\theta\cos\theta+\sqrt3\cos\theta=0\)
geerky42
  • geerky42
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?
BloomLocke367
  • BloomLocke367
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

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More answers

geerky42
  • geerky42
WWhat answer do you have?
geerky42
  • geerky42
\(\dfrac{\pi}{2}\) and \(\dfrac{3\pi}{2}\), right?
BloomLocke367
  • BloomLocke367
pi/2 and 3pi/2. I used the unit circle to find the values for when cos=0
BloomLocke367
  • BloomLocke367
yes
geerky42
  • geerky42
ok. now we solve for \(2\sin\theta+\sqrt3 = 0\) Try isolate \(\sin\theta\).
geerky42
  • geerky42
Then use unit circle
BloomLocke367
  • BloomLocke367
ohhh \(\sin\theta=-\sqrt3/2\) so the answers are \(\Large\frac{5\pi}{6}\) and \(\Large\frac{7\pi}{6}\)
BloomLocke367
  • BloomLocke367
right?
BloomLocke367
  • BloomLocke367
wait... I used cos, not sin
BloomLocke367
  • BloomLocke367
the answers are \(\Large\frac{4\pi}{3}\) and \(\Large\frac{5\pi}{3}
BloomLocke367
  • BloomLocke367
oops
geerky42
  • geerky42
Right.
BloomLocke367
  • BloomLocke367
\(\Large\frac{5\pi}{3}\)
BloomLocke367
  • BloomLocke367
thank you!! some more?
geerky42
  • geerky42
sure

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