## BloomLocke367 one year ago question below!

1. BloomLocke367

What values for $$\Large\theta(0\le\theta\le2\pi)$$ satisfy the equation? $$\Large2\sin\theta\cos\theta+\sqrt3\cos\theta=0$$

2. 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?

3. 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

4. geerky42

5. geerky42

$$\dfrac{\pi}{2}$$ and $$\dfrac{3\pi}{2}$$, right?

6. BloomLocke367

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

7. BloomLocke367

yes

8. geerky42

ok. now we solve for $$2\sin\theta+\sqrt3 = 0$$ Try isolate $$\sin\theta$$.

9. geerky42

Then use unit circle

10. BloomLocke367

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

11. BloomLocke367

right?

12. BloomLocke367

wait... I used cos, not sin

13. BloomLocke367

the answers are $$\Large\frac{4\pi}{3}$$ and $$\Large\frac{5\pi}{3} 14. BloomLocke367 oops 15. geerky42 Right. 16. BloomLocke367 \(\Large\frac{5\pi}{3}$$

17. BloomLocke367

thank you!! some more?

18. geerky42

sure