Help with a Trigonometric equation?

[brinazarski]

EDIT: NEW QUESTION AT LATEST POST!

EDIT: NEVERMIND!!! My factoring was off! Sorry ><;; I'm still working on this homework so I'll bump it if I still have questions

2cos²x + cosx - 1 = 0


I got (2cos + 1)(cos - 1) = 0


2cos + 1 = 0
2cos = -1
cos = -1/2
cos = 120 degrees


and


cos - 1 = 0
cos = 1
cos = 0 degrees


But the answer is apparently 60, 180, and 300, so I am VERY off... help? Explain how to do this?

 

[brinazarski]

​Nvm again, Yahoo! Answers helped me~

NEW QUESTION! cosxsinx + sinx = 0

sinx(cosx + 1) = 0

cosx + 1 = 0
cosx = -1
cos = 180 degrees

sinx = 0
sin = 0 degrees

So the answers are 0 and 180... but according to my answer key it's also 360. Where does the 360 come from?

 

[brinazarski]

OKAY! NEW QUESTION AGAIN! Unless Yahoo! Answers beats this site again...

tan2x = 4tanx


I got 0 and pi (it has to be in rads), but there are several more answers. I did it with a calculator by graphing... is there are way to do this algebraically? Please explain ><;

 

[Deleted member 4993]

OKAY! NEW QUESTION AGAIN! Unless Yahoo! Answers beats this site again...

tan2x = 4tanx


I got 0 and pi (it has to be in rads), but there are several more answers. I did it with a calculator by graphing... is there are way to do this algebraically? Please explain ><;

I have no interest in competing with Yahoo answers.

We do not give you answers - we provide hints. Then you do the work - if you are stuck again - you would show work and we will give hints again...

hint for the problem above:

write tan(2x) as a function of tan(x) and simplify then solve for x.

 

[brinazarski]

I know, I'm just saying, I post here and Yahoo at the same time, and if they answer my question first then I don't need help And I'm not interested in answers, I have them in my textbook, I just want to know HOW to get them, so the hints are helpful

But, I'm still confused.

tanx + tanx / 1 - tan^2x = 4tanx/1

tanx + tanx = 4tanx - 4tan^3x

tanx + tanx = 4tanx(1 - 4tan^2x)

I am soooo lost, I'm sorry... did I do it right so far? May I get another hint? ><

 

[Deleted member 4993]

I know, I'm just saying, I post here and Yahoo at the same time, and if they answer my question first then I don't need help And I'm not interested in answers, I have them in my textbook, I just want to know HOW to get them, so the hints are helpful

But, I'm still confused.

tanx + tanx / 1 - tan^2x = 4tanx/1

tanx + tanx = 4tanx - 4tan^3x

tanx + tanx = 4tanx(1 - 4tan^2x)

I am soooo lost, I'm sorry... did I do it right so far? May I get another hint? ><

Hints:

tan(x) + tan(x) = 2 * tan(x)

4*tan(x)/(2*tan(x)) = 2