anonymous
  • anonymous
Find all solutions to the equation. cos2x + 2 cos x + 1 = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Nnesha
  • Nnesha
let cosx = x then deal with it as quadratic equation \[\huge\rm x^2 +2x +1 =0\]
Nnesha
  • Nnesha
can you u factor it ?
anonymous
  • anonymous
So it is like (x+1)(x+)1.

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anonymous
  • anonymous
the 1 should be on the parenthesis*
Nnesha
  • Nnesha
yes right set it equal to zero
anonymous
  • anonymous
It'll be -1.
Nnesha
  • Nnesha
x = -1 so now we can change x to cos x cos x = -1
anonymous
  • anonymous
Is pi the only solution?
Nnesha
  • Nnesha
yep right or -1 has multiplicity of 2 bec cox = -1 , cosx =- 1 are solution
Nnesha
  • Nnesha
yes right cos x = -1 = pi
anonymous
  • anonymous
Uhm do I have to put pi+2 pi n as the solution or just pi?
Nnesha
  • Nnesha
pi +2 ?
Nnesha
  • Nnesha
just pi
Nnesha
  • Nnesha
\[\pi + 2 \cancel =\pi \]
anonymous
  • anonymous
I know that haha, but base on my textbook, "Method for Solving Trigonometric Equations Unless the equation is factorable, use substitution to get just one trigonometric function. Solve the equation for the trigonometric function. Solve for the variable in a general window of +2pin for sine and cosine and +pin for tangent. Find the specific solutions in the given interval by replacing n with integers."
anonymous
  • anonymous
So I'm kinda confused.
Mertsj
  • Mertsj
It said to find all solutions. One solution is pi. Another solution is 3pi. Another solution is 5pi... We write that like this: \[x=\pi+2\pi n\]
anonymous
  • anonymous
@Mertsj That's what I'm talking about lol thank you for the help guys!
Mertsj
  • Mertsj
yw
Nnesha
  • Nnesha
cool i didn't know this x = pi + 2pi n thingy

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