A community for students.
Here's the question you clicked on:
 0 viewing
marasofia1616
 2 years ago
Find all solutions to the equation.
cos2x + 2 cos x + 1 = 0
marasofia1616
 2 years ago
Find all solutions to the equation. cos2x + 2 cos x + 1 = 0

This Question is Closed

rsnoob
 2 years ago
Best ResponseYou've already chosen the best response.0For cos(2x) * (2cos(x) + 1) = 0, use the double angle identity for cos(2x), which is cos^2 x  sin^2 x = cos^2 x  (1cos^2) = 2cos^2 x  1. So we have (2cos^2 x  1)(2cos x + 1) = 0. So 2cos^2 x 1 = 0 or x = 0 and 2pi. For 2sec^2 x + tan^2 x  3 = 0, use the identity sec^2 x = tan^2 x + 1, so we have 2(tan^2 x + 1) + tan^2 x  3 = 0 or 2tan^2 x + tan^2 x  1 = 0 or 3 tan^2 x = 1. So x = pi/2, pi/2 + pi = 3pi/2.

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1hi the first thing I tried to solve this problem was to factor it so I have (cos x+1)(cos x+1) but now I dont know what to next

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0Unclear how to proceed. What is the first term, \(\cos(2x)\) or \(\cos^{2}(x)\)?

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1cos \[\cos^{2}x\]

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0Perfect. The we have only to solve  by factoring. \(\cos^{2}x + 2\cos x + 1 = 0\) \((\cos(x) + 1)^{2} = 0\) Now what?

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1That is where I got stuck I am not sure what to do after factoring

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0What's the point of factoring? Why do we do that at all? If a*b = 0, what do we know about a or b? To contract, if a*b = 4, what do we NOT know about either a or b?

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1what each of the equal?

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0Kind of. a*b = 0 tells us that either a = 0 or b = 0. What can we tell about a and b when it isn't zero? a*b = 4, for example? Is one of them zero? Aboslutely not, but that's about all we can tell. Is a = 4? Maybe. Is b = 12? Maybe. Not a clue. Only "=0" is particularly helpful. So, what should we do with that factored expression?

chaguanas
 2 years ago
Best ResponseYou've already chosen the best response.0tkhunny your explanations are more complex than the problem itself :)

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0That's why we invent notation, so that problems can be simpler than explanations. If we have this: Factor1 * Factor2 = 0 Then we must have Either this Factor1 = 0 or this Factor2 = 0 How can we apply this to your factored equation?

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1cos x+1(0)=0 I am not sure

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0\((\cos(x)+1)^{2} = 0\) We have two factors, but hey are exactly the same. This limits the possible results. \(\cos(x) + 1 = 0\) \(\cos(x) = 1\) \(x = \dfrac{3\pi}{2} + 2k\pi\) where \(k\in \mathbb{Z}\) Do you know what all that means?

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1I do... but if cos(x)=1 wouldn't [x=\pi\]

marasofia1616
 2 years ago
Best ResponseYou've already chosen the best response.1anyway I got it ... thanks for the help!

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0Awesome. How did I do that?! Right you are. \(x = \pi + 2k\pi\)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.