helpplease1 Group Title 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 one year ago one year ago

1. looser66 Group Title

still need help?

yes i do :(

3. looser66 Group Title

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 Group Title

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 Group Title

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 Group Title

you should post the original one, friend.

11. looser66 Group Title

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 Group Title

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 Group Title

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

x=-5/2 and x=1?

18. looser66 Group Title

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 Group Title

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 Group Title

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 Group Title

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