Question

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

Answer 1

still need help?

Answer 2

yes i do :(

Answer 3

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 \(\theta\)

Answer 4

thank you! but i mistyped the question it is actually plus 3, not 1. :(

so would the quadratic equation be \[2x ^{2}-3x+3\]?

Answer 5

i cannot figure out how to factor that

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

you should post the original one, friend.

Answer 11

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

Answer 12

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

Answer 13

hahaha no ph.d student here

Answer 14

so? everything is quite simple, right?

Answer 15

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

Answer 16

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

Answer 17

x=-5/2 and x=1?

Answer 18

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

Answer 19

okay. so: cos(theta)=1?

how do i make the general formula in form of of: _+_k

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

oh my gosh thank you so much for your help!

Answer 24

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

Answer 25

:) :)