## anonymous one year ago what values for theta(0≤theta≤2pi) satisfy the equation? 2sinthetacostheta+sqrt 3 theta

1. freckles

is there an equation?

2. anonymous

yeah

3. anonymous

4. freckles

ok so you meant to put =0 at the end

5. anonymous

yeah

6. anonymous

I'm really confused x.x why r practice packets so hard >:C

7. freckles

and the other cos thingy but yeah anyways you can factor the left hand side $2 \sin(\theta)\cos(\theta)+\sqrt{3} \cos(\theta)=0 \\ \text{ factor out the } \cos(\theta) \\ \cos(\theta)[2 \sin(\theta)+\sqrt{3}]=0$

8. freckles

set both factors =0 and solve for theta

9. freckles

$\cos(\theta) \text{ or } \sin(\theta) =\frac{-\sqrt{3}}{2}$ use unit circle

10. anonymous

??!!

11. freckles

forgot the =0 part :p

12. freckles

$\cos(\theta)=0 \text{ or } \sin(\theta) =\frac{-\sqrt{3}}{2}$ use unit circle *

13. anonymous

??? wits the answer suppose to be :( explanation too pls

14. freckles

sin(theta) is the y-coordinate on the unit circle find for what theta's you have the y value ( the second value) of the pair is -sqrt(3)/2

15. freckles

hint: look in quadrants 3 and 4

16. anonymous

okie :( wait the answer is B??

17. freckles

sin(3pi/4) is not -sqrt(3)/2 it is sqrt(2)/2

18. anonymous

19. freckles

i didn't say that i just said the option you chose is incorrect because sin(3pi/4) is not -sqrt(3)/2

20. freckles

did you look at the unit circle you are looking for when the y-coordinate is -sqrt(3)/2

21. anonymous

D

22. freckles

the hint I gave is to look in the 3rd and 4th quadrant

23. anonymous

d??

24. freckles

https://www.mathsisfun.com/geometry/images/circle-unit-radians.gif look at this picture do you see the ordered pairs?

25. freckles

look at the second number of each pair you are looking to for which theta you have the y coordinate is -sqrt(3)/2

26. freckles

can you tell me looking at that chart thing where you see y coordinate is -sqrt(3)/2

27. anonymous
28. freckles

ok look at that chart do you see under sin -sqrt(3)/2 ?

29. freckles

find it then use your finger and move it horizontally from that number to the theta number

30. anonymous

OH I GET WUT MEAN ITS A DUH ITS 4PI/3 IM SO STUPID

31. freckles

yes sin(4pi/3)=-sqrt(3)/2

32. freckles

and sin(5pi/3)=-sqrt(3)/2

33. freckles

and of course cos(theta)=0 is easy to solve and all of the choices included its answers which was pi/2 and 3pi/2

34. anonymous

:D thnx so much here a medal

35. freckles

np