Help with Trig Equations! (1 Viewer)

[Sugar]

Solve:

1) 2tan2x -1 = 0, 0 < x < 360 (degrees)

I got x = 13'17' and 103'17', but there are 4 answers (13'17', 103'17', 193'17', 283'17') . Can anyone explain why?

And also, why don't you double the quadrant ( 0 < 2x < 720)?

2) 2tanx + 3 = 0

Similar the q1, I only got two of the four answers.

Thanks in advance.

 

[FinalFantasy]

Solve:

1) 2tan2x -1 = 0, 0 < x < 360 (degrees)

I got x = 13'17' and 103'17', but there are 4 answers (13'17', 103'17', 193'17', 283'17') . Can anyone explain why?

And also, why don't you double the quadrant ( 0 < 2x < 720)?

2) 2tanx + 3 = 0

Similar the q1, I only got two of the four answers.

Thanks in advance.

1)2tan2x=1
tan2x=1\2
2x=26'34', 206'34', 386'34', 566'34'
x=13'17', 103'17', 193'17', 283'17'
u need to keep going with the 2x=..... cuz u won't get all da stuff in da required domain if u don't.

similar for q.2

 

[Sugar]

Oh, thanks FinalFantasy!

 

[namelesslady]

Because it's tan2x, don't you have to test two revolutions? Because, even though it's between 0 and 360, you'll still get answers in the parameters? I know the question's already been answered already, but I have a test on this topic on Friday, and I want to check that I'm right.

 

[FinalFantasy]

just keep going until u can c dat u can divide it by 2 and it would be in da required domain. or ur test for "two revolutions" is ok i guess...

 

[Trebla]

When dealing with half angles, double angles, triple angles etc, you must expand or reduce your domain.
For example if the domain asked in the question was 0 < x < 360, then 0 < 2x < 720 and 0 < x/2 < 180 and so on, depending on the question. After you got your answers in the modified domain you MUST simplify it in terms of what solution(s) the question is asking for. At the end check if it satisfies the required domain in the question.
i.e. in terms of your questions:
1) 2tan2x - 1 = 0 (for 0 < x < 360)
your new domain is now 0 < 2x < 720 {since you are working with 2x}
tan 2x = 1/2
.: 2x = 26'34', 206'34', 386'34', 566'34' (for 0 < 2x < 720)
.: x = 13'17', 103'17', 193'17', 283'17' (for 0 < x < 360)
[see how the solutions satisfy the domain and are still correct when you substitute it back in]

By the way shoudn't question 2 only have two answers if the domain is 0 < x < 360?
Since tan x is negative, then using ASTC rule then there should be only two solutions not four.