## helpplease1 2 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. looser66

still need help?

yes i do :(

3. looser66

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 $$\theta$$

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

i cannot figure out how to factor that

6. looser66

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

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

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

9. looser66

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. looser66

you should post the original one, friend.

11. looser66

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

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

hahaha no ph.d student here

14. looser66

so? everything is quite simple, right?

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

16. looser66

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

x=-5/2 and x=1?

18. looser66

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

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

20. looser66

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

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

22. looser66

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

oh my gosh thank you so much for your help!

24. looser66

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