## anonymous 3 years ago Determine the general formula(s) for the solution. Then, determine the specific solutions on the interval [0,2pi). 2cos^2(theta)-3cos(theta)+1=0

1. anonymous

still need help?

2. anonymous

yes i do :(

3. anonymous

let cos$$\theta$$= x, you have the form of $$2x^2-3x+1=0$$ solve for x as a quadratic equation, then plulg back to x = cos $$\theta$$ to solve for $$\theta$$

4. anonymous

thank you! but i mistyped the question it is actually plus 3, not 1. :( so would the quadratic equation be $2x ^{2}-3x+3$?

5. anonymous

i cannot figure out how to factor that

6. anonymous

which class are you in? do you know Euler's formula for complex number?

7. anonymous

i am just in a college trig class. 1316. we have not gotten to euler's formula thus far

8. anonymous

this is the actual problem $2\sin ^{2}\Theta-3\cos \Theta=-3$

9. anonymous

hey, it totally different,!! heehe , let see. 2 sin^2 = 2 - 2cos^2 therefore, 2-2cos^2 -3 cos +3 =0 2cos^2 +3 cos -5 =0, can solve it now

10. anonymous

you should post the original one, friend.

11. anonymous

you really scared me!! I thought I met a Ph.D student.

12. anonymous

lol i know i got it confused with another problem. I was really good at algebra but this stuff is just killing me...

13. anonymous

hahaha no ph.d student here

14. anonymous

so? everything is quite simple, right?

15. anonymous

so i have $2x ^{2}+3x-5=0$ and now factor? im sorry this class has confused me so much

16. anonymous

if you know how to factor, do it. if not, use discriminant. Either way is ok.

17. anonymous

x=-5/2 and x=1?

18. anonymous

yes, and reject -5/2, out of interval

19. anonymous

okay. so: cos(theta)=1? how do i make the general formula in form of of: _+_k

20. anonymous

not finish yet, cos $$\theta$$ =1 $$\rightarrow \theta$$ = 0 + 2k$$\pi$$ that 's the general formula solution for you

21. anonymous

so the only solution is 0? because subbing 1 for k would make 2pi which would not be included in the interval?

22. anonymous

yes, you are right. general form is 2kpi, specific solution in the interval is 0 Medal for a good student

23. anonymous

oh my gosh thank you so much for your help!

24. anonymous

do I help? No! just you work on it, I did nothing. hehee

25. anonymous

:) :)

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