# Thread: cos5x=0 waaaaaaaaaaaaah

1. ## cos5x=0 waaaaaaaaaaaaah

could someone explain this working,makes no sense to me,Q is solve sin5x=0 in range 0 to 2pie inclusive, giving roots as ,multiples of pi

sin5x=0 implies 5x=kpie , k=0 to 9
implies x=kpie/5 therefore k=0 to9

i dont have a clue about this does sum 1 know???

2. Hello,

sin5x=0 implies 5x=kpie , k=0 to 9
implies x=kpie/5 therefore k=0 to9
I don't understand your writing, though the result is (almost) correct. But the "therefore" part makes no sense...

Let X=5x. Then X is between 0 and 10 pi.
So you have to solve for sin(X)=0

As you said, X=k*pi, with k=..., -2, -1, 0, 1, 2, ....

Since X is between 0 and 10 pi, therefore k=0, 1, ..., 9, 10 (0 and 2 pi are inclusive).

Solutions are $X=0, \ \pi, \ 2 \pi, \dots , \ 9 \pi, \ 10 \pi$

---> $x=0, \frac{\pi}{5}, \frac{2 \pi}{5}, \dots , \frac{9 \pi}{5}, 2 \pi$

Is it ok ? oO

3. Originally Posted by Moo
Hello,

I don't understand your writing, though the result is correct. But this implication makes no sense...

Let X=5x. Then X is between 0 and 10 pi.
So you have to solve for sin(X)=0

As you said, X=k*pi, with k=..., -2, -1, 0, 1, 2, ....

Since X is between 0 and 10 pi, therefore k=0, 1, ..., 9, 10 (0 and 2 pi are inclusive).

Solutions are $X=0, \ \pi, \ 2 \pi, \dots , \ 9 \pi, \ 10 \pi$

---> $x=0, \frac{\pi}{5}, \frac{2 \pi}{5}, \dots , \frac{9 \pi}{5}, 10 \pi$

Is it ok ? oO
Last one should be $\frac{10\pi}{5}$

Right? Probably just a typo.

4. first of all try to give a meaningful title to your post instead of :

and avoid using chat language such as:
does sum 1 know
------------------------------------------------------------------------

$\begin{gathered}
\sin 5x = 0 \hfill \\
\Leftrightarrow 5x = \pi k,\quad k \in Z \hfill \\
\Leftrightarrow x = \frac{\pi }
{5}k \hfill \\
\end{gathered}
$

now we are interested in the answers which are in the following interval [0, 2pi]:

$\begin{gathered}
0 \leqslant \frac{\pi }
{5}k \leqslant 2\pi \hfill \\
\hfill \\
\leftrightarrow 0 \leqslant k \leqslant 10 \hfill \\
\end{gathered}$