## anonymous one year ago Need some Trig HElp

1. anonymous

what do you need help with?

2. anonymous

i will attach the file, give me a second

3. anonymous

4. anonymous

@dan815

5. anonymous

@jim_thompson5910

6. DanJS

hmm, try replacing cos^2 with 1 - sin^2

7. anonymous

which attachment are you on

8. DanJS

the first one...

9. DanJS

$3\sin(\theta)+3 = 2\cos^2(\theta)$

10. anonymous

ok

11. anonymous

i did that

12. DanJS

ok, it looks like you can factor that now if you put it in ax^2+bx+c form , with the x being sin

13. DanJS

$2\sin^2(\theta)+3\sin(\theta)+1=0$

14. anonymous

wait but this is what my equation looks like so far... is it right

15. anonymous

@DanJS

16. DanJS

right, from the unit circle , there is the property, sin^2 + cos^2 = 1, that is what we did

17. DanJS

then just simplify that down to

18. DanJS

$2\sin^2(\theta)+3\sin(\theta)+1=0$

19. anonymous

ok got it

20. DanJS

so you can factor that like usual quadratics , let v=sin(theta) 2v^2 + 3v + 1 = 0

21. anonymous

ok give me a sec

22. DanJS

$(v+1)(2v+1)=0$

23. DanJS

replace v back with sin(theta) $(\sin \theta + 1)(2\sin \theta +1) = 0$

24. DanJS

good so far?

25. anonymous

yeah

26. DanJS

that is true if either of those parenthesis terms are zero, so you have $\sin(\theta) = -1~~~or~~~\sin(\theta) = -1/2$

27. DanJS

do you know how to figure those from the unit circle?

28. anonymous

yeah, but im kind of weak in my unit circle so i might get it wrong

29. DanJS

Ill tell ya, soon as you get that picture, everything clicks good...

30. anonymous

ok should I gust google unit circle

31. DanJS
32. DanJS

do you want a quick rundown of it, how to determine angles

33. anonymous

no i got it

34. anonymous

i just needed a brush up

35. anonymous

the picture is fine

36. DanJS

aight, what are the answers for this one

37. anonymous

the answers are -pi/2, 3pi/2, -pi/6, 7p/6

38. DanJS

read the problem one more time through...

39. anonymous

oh so it is just 3pi/2 and 7pi/6

40. DanJS

not quite... lets look at the first one... sin(theta) = -1 Each point on the circle is the coordinate (cos , sin) , the y coordinate is the sin of the angle... y is -1 at 270 or 3pi/2

41. DanJS

for sin(theta) = -1/2 there are 2 angle values where the y coordinate is -1/2

42. DanJS

|dw:1438716059055:dw|

43. anonymous

ahhhh

44. DanJS

i remember taking trig and never got how angles were figured till this circle pic , after the class was over

45. DanJS

radius is 1, so sin = opp/hyp = opp/1 = opp , or the y coordinate

46. anonymous

ok that makes sense

47. DanJS

48. anonymous

49. DanJS

welcome

50. anonymous

so the solutions to the equation are?

51. anonymous

@DanJS

52. anonymous

@Loser66 can you help me with my other questions