Trigonometric inequality

[learningmathh]

I want to solve this

\(\displaystyle 4cos(x)+2< 0\rightarrow cos(x)< -1/2\)
when x is between \(\displaystyle [0, 2\pi]\)

And cos (x)=-1/2 is 2pi/3 and 4pi/3 so x is between those two like \(\displaystyle 2\pi/3< x< 4\pi/3\)
, right? So why does the book say \(\displaystyle 0\leq x< 2\pi/3and\rightarrow 4\pi/3< x\leq 2\pi\)

I dont understand, is the book wrong, anyone?

 

[stapel]

I want to solve:

\(\displaystyle 4cos(x)+2< 0\rightarrow cos(x)< -1/2\) when x is between \(\displaystyle [0, 2\pi]\)

And cos (x)=-1/2 is 2pi/3 and 4pi/3 so x is between those two like \(\displaystyle 2\pi/3< x< 4\pi/3\)

The two zeroes split the interval into three sub-intervals. How are you concluding that, of the three sub-intervals, you want the one in the middle instead of the two on the ends? What did you see when you looked at the graph?

 

[Ishuda]

I want to solve this

\(\displaystyle 4cos(x)+2< 0\rightarrow cos(x)< -1/2\)
when x is between \(\displaystyle [0, 2\pi]\)

And cos (x)=-1/2 is 2pi/3 and 4pi/3 so x is between those two like \(\displaystyle 2\pi/3< x< 4\pi/3\)
, right? So why does the book say \(\displaystyle 0\leq x< 2\pi/3and\rightarrow 4\pi/3< x\leq 2\pi\)

I dont understand, is the book wrong, anyone?

Looks like someone got the inequality sign reversed

 

[Dale10101]

I think I see your point.

I want to solve this

\(\displaystyle 4cos(x)+2< 0\rightarrow cos(x)< -1/2\)
when x is between \(\displaystyle [0, 2\pi]\)

And cos (x)=-1/2 is 2pi/3 and 4pi/3 so x is between those two like \(\displaystyle 2\pi/3< x< 4\pi/3\)
, right? So why does the book say \(\displaystyle 0\leq x< 2\pi/3and\rightarrow 4\pi/3< x\leq 2\pi\)

I dont understand, is the book wrong, anyone?

You say "x is between those two like \(\displaystyle 2\pi/3< x< 4\pi/3\)".

I see your point, x = pi is between (2/3)pi and (4/3) pi, the cosine of pi is -1, -1 is less then -1/2 on the number line.

If x = pi, 4Cos(pi) + 2 = 4(-1) +2 = -2 < -1/2, check.

I think the question being raised with regard to the book answer is whether or not you have transcribed the problem to be solved correctly?