Question

question below!

Answer 1

What values for \(\Large\theta(0\le\theta\le2\pi)\) satisfy the equation?

\(\Large2\sin\theta\cos\theta+\sqrt3\cos\theta=0\)

Answer 2

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?

Answer 3

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

Answer 4

WWhat answer do you have?

Answer 5

\(\dfrac{\pi}{2}\) and \(\dfrac{3\pi}{2}\), right?

Answer 6

pi/2 and 3pi/2. I used the unit circle to find the values for when cos=0

Answer 7

yes

Answer 8

ok. now we solve for \(2\sin\theta+\sqrt3 = 0\)

Try isolate \(\sin\theta\).

Answer 9

Then use unit circle

Answer 10

ohhh \(\sin\theta=-\sqrt3/2\) so the answers are \(\Large\frac{5\pi}{6}\) and \(\Large\frac{7\pi}{6}\)

Answer 11

right?

Answer 12

wait... I used cos, not sin

Answer 13

the answers are \(\Large\frac{4\pi}{3}\) and \(\Large\frac{5\pi}{3}

Answer 14

oops

Answer 15

Right.

Answer 16

\(\Large\frac{5\pi}{3}\)

Answer 17

thank you!! some more?

Answer 18

sure