## anonymous 5 years ago 3x^2-7x-3=0

1. amistre64

3times3 is 9 which doesnt factor into 7.... so quadratic it :)

2. anonymous

after using the quadratic formula, how do you complete the problem?

3. amistre64

that is the completed problem. you could try doing the "complete the square" method; but all that method does is prove that the quad formula works.

4. anonymous

my textbook says to find the nearest degree.. x = sin of theta

5. amistre64

then find what x equals and take the sine inverse of it. the inverse trig funtions take numbers for inputs and spit back angles. Does that make sense?

6. anonymous

not really :/

7. amistre64

lets walk you thru it then :) first get the values for x with the quad formula. 7/6 (+-) sqrt(49-(4)(-3)(3))/ 6 7/6 (+-) sqrt(49+36)/6 7/6 (+-) sqrt(85)/6 you with me so far?

8. anonymous

ok, let me see.

9. anonymous

where do you get 49?

10. amistre64

the quad form reads: -middle (+-) sqrt(middle^2 -4(first)(last)) all over 2(first). or more formally: -b (+-) sqrt(b^2-4(a)(c)) --------------------- 2(a) right? -7 times -7 = 49

11. anonymous

oh. it's b^2? no wonder i never got any solution out of that. thank you very much! +5

12. amistre64

we got numbers for our x now; (7/6 (+-) sqrt(85)/6) if I did it correctly right?

13. anonymous

umm.. i'm still solving it. i got the b^2 correct

14. anonymous

my calculator says -49 instead of 49. so weird～

15. amistre64

lol.... maybe user error? To find out what sin(t) is when x equals some number we write it like this: sin(t) = x To find out what "t" is we need to get rid of the (sin) part. And we do that by using what is called the sine inverse function.

16. anonymous

i think it was supposed to be 7 not -7

17. amistre64

all it changes in the end is the sign of (7/6) to (-7/6) which may or may not be an issue

18. anonymous

got it. $x=7\pm \sqrt{49+36} \div 6$

19. amistre64

if your equation you gave was correct, then it was supposed to be (-7)^2 = 49. But (7)^2 = 49 just the same

20. amistre64

good :) you ready to learn about sin inverse? its symbol is (sin^-1)

21. anonymous

i know sin^-1 but i'm stuck in where should i go next.

22. amistre64

lets walk it thru. It asks us to find sin(t) = x right?

23. anonymous

sin $\theta$

24. amistre64

theta is simply a name, I will make it simpler and just name it "t" do you think I can do that?

25. anonymous

yea, sure. :)

26. amistre64

lol...good, mathmaticians like to rename things all the time, makes them feel important :)

27. anonymous

XD

28. amistre64

we have: sin(t) = x we need to get rid of the "sin" part. So lets apply sin^-1 to each side to get: t = sin^-1(x) Now plug the numbers into your scientific calculator to get an angle for t, formally known as theta

29. anonymous

wait. i'm confused here. do i continue with the quad. formula?

30. amistre64

the quad formula simply gave us the values for x....its job is done and it can go take a well deserved break...

31. anonymous

so i continue with this:$3\sin^2\theta-7\sin \theta-3=0$

32. amistre64

aha!!! you were holding back vital information...hmmm

33. anonymous

opps.. am i in trouble?

34. amistre64

nah....just makes the problem more understandable now :)

35. anonymous

XD. so how do i continue?

36. amistre64

just the same as before :) sin(t) = x and solve for t But I gotta tell wonder, do you have the problem written correctly becuase I get some wierd stuff when I plug it into the calculator..

37. anonymous

the textbook says to use the quadratic formula to find,to the nearest degree, all values of theta in the interval 0 degrees [less than or equal to] theta [less than] 360 degrees that satisfy each equation.

38. amistre64

338.29 degrees is what I get, which is in Quad4 but it is also hiding in Quad3 under the disguise of 201.71 degrees.

39. amistre64

[7+sqrt(85)] /6 is greater then 1 so it spits out an error. x = 2.7 and that aint between -1 and 1 so it is a false reading.

40. amistre64

[7-sqrt(85)]/6 = -0.3699 which IS between -1 and 1 so it is a good value of x.

41. amistre64

is there anyway to verify the answer?

42. anonymous

i got the same answer as you. -0.3699240762

43. amistre64

either were both geniuses or were both idiots...take your pick :)

44. anonymous

GENIUS! :D

45. amistre64

yay!!!

46. amistre64

the thing about sin^-1 is that it only gives an angle that is on the right hand side of a circle. So you have to remember to look over to the other sid eto see where it matches up at.

47. amistre64

does any of that make sense to you?

48. anonymous

somewhat, let me think over~

49. anonymous

i think i got it, thanks for helping me though(: