## anonymous 5 years ago Solve this equation on the interval 0$\le$ θ < 2π. If there is only one solution, write it in the upper box and write NONE in the lower box. If there is no solution, write NONE in both boxes. Round your answer(s) to two decimal places using radians. θ = (smaller value of θ) θ = (larger value of θ)

1. amistre64

there is no equation here...

2. anonymous

haha really? why is that?

3. amistre64

Its alot of instructions on what to do; but there is no equation to work it on lol

4. anonymous

lol!! sorry!!

5. anonymous

i got it here

6. anonymous

sintheta + sqrt3costheta = 1

7. amistre64

sin(t) + sqrt(3)cos(t) = 1 right?

8. anonymous

yes

9. amistre64

then.... sqrt(3)cos(t) = 1 - sin(t) 3cos^2 = 1 +sin^2 -2sin... lets cheat and do this lol http://www.wolframalpha.com/input/?i=sin%28t%29+%2B+sqrt%283%29cos%28t%29+%3D+1

10. anonymous

hahaha thats the way!

11. anonymous

damn it im not gettin it!

12. amistre64

i cant seem to get it out either.... i know theres one answer at least; might have to just make a chart and narrow it in

13. anonymous
14. amistre64

an alternative form is: $4\sin[\frac{\pi}{4}-\frac{t}{2}] . \sin[\frac{t}{2}+\frac{\pi}{12}]=0$

15. anonymous

ohkay...lol

16. amistre64

since sin = 0 at 0 and pi; we can prolly figure out a few t's from this ?

17. amistre64

t/2 = pi/4 t = pi/2sounds reasoneable plug it into the orifinal and test

18. anonymous

i think ur getin somewhere haha

19. amistre64

the other seems to be -pi/6 but that aint in the inteval is it lol

20. anonymous

lol no it isnt haha

21. amistre64

sin(pi / 2) + (sqrt(3) * cos(pi / 2)) = 1 is good tho

22. anonymous

would that be the lower value or upper value?

23. amistre64

thats the lower value

24. anonymous

i only get two shots so i probably beta wait till we figur out the upper value lol

25. amistre64

its close to 2pi according to the graph

26. amistre64

now we know -pi/6 is good; but if we take and try to reach that going from 0 to 2pi what do we get? i wonder

27. amistre64

11pi/6 right?

28. amistre64

sin((11 * pi) / 6) + (sqrt(3) * cos((11 * pi) / 6)) = 1: from google

29. anonymous

howd u get tht?

30. anonymous

11pi/6 from -p1/6 ?

31. amistre64

all angles have many names to them because when you walk around a circle you can go along way and still get nowhere

32. amistre64

we can walk -pi/6 to smell the roses; or we can take the long way around; and walk 11pi/6 to get to the same place to wmell the roses

33. anonymous

lol. so u added two pi?

34. amistre64

I did ;)

35. anonymous

haha. it works doesnt it?

36. amistre64

it does indeed :) becuase they both have the same values

37. anonymous

kay so u reckon i should give pi/2 and 11pi/6 a shot?

38. amistre64

i do..

39. anonymous

yay ur a genius!!! it works haha

40. amistre64

lol .... i had to remember my trigs :)

41. anonymous

haha. is there a simpler way of doing this tho?

42. amistre64

i caouldnt find a way to get it into the alternate form; but wolfram did... so i tested that forms results into the original and they worked like a charm

43. anonymous

good ole wolfram lol

44. anonymous

so are you a teacher?

45. amistre64

no, just old :) im trying to get my masters degree in math tho so I can teach college math

46. anonymous

good effort. you'll get there mate haha