SOLUTION: Find all solutions in degress in the interval [0,360] 6cos^2x+7cosx+2=0 Thank you friends

Algebra.Com
Question 1101265: Find all solutions in degress in the interval [0,360]
6cos^2x+7cosx+2=0
Thank you friends

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
It's a quadratic in cos(x)
Check for extraneous solutions.
Answer by ikleyn(52909)   (Show Source): You can put this solution on YOUR website!
.
Instruction from Alan is correct, but I think that for the person who posted it, it is not enough.


So I put the entire solution here.


Introduce new variable u = cos(x). Then your equation takes the form

6u^2 + 7u + 2 = 0.


It is QUADRATIC EQUATION for the unknown "u". To solve it, apply the quadratic formula

 =  = .


You have two solutions for u:


1)   =  =  = .

    It leads us to equation cos(x) =  which has TWO solutions x = 120 degs and/or x = 240 degs in the given interval.


2)   =  =  = .

     It leads to equation cos(x) =  which has TWO solutions x = arccos(-2/3) degs and/or x = arccos(-2/3) degs + 180 degs  in the given interval.


Answer.  The given equation has 4 (four) solutions:

         x= 120 degs;  x= 240 degs;  x= arccos(-2/3) degs  and  x = arccos(-2/3) degs + 180 degs.

Solved.



RELATED QUESTIONS

Find all solutions in the interval [0, 2π) {{{ sec^2(x)+6tan(x)=6 }}} Thank... (answered by Alan3354,Edwin McCravy)
Approximate to the nearest degree, the solutions of the equation in the interval [0°,... (answered by lwsshak3)
find all the solutions in the interval [0, 360 degrees) for... (answered by Fombitz)
I need help figuring out this trigonometry problem. Fin,d to the nearest degree, all... (answered by stanbon)
Find all the solutions in the interval [0, 2𝜋) cos^2(x)+2cos(x)+1=0 Thank... (answered by MathLover1)
could you help me find all the solutions in the interval [0, 2pi)... (answered by lwsshak3)
Use your graphing calculator to find all degree solutions in the interval 0° ≤ x <... (answered by Theo,ikleyn,greenestamps)
Find all possible solutions: a.) 7cosx = 4 - 2sin^2x b.) 2sec^2x + tan^2x = 3... (answered by stanbon)
The solutions of cos 2x = 0, in the interval 0 < x <... (answered by nerdybill)