Question

Points of intersection with x-axis?

Answer 1

How do I find the points of intersection with the x-axis of the function \[y=\frac{ 1 }{ 2 }\sin 3\theta\]

Answer 2

I couldn't find how to do this in my book. please help. @phi

Answer 3

You simply need set y to zero. So you get that:
\[0 = \frac{1}{2} \sin(3 \theta) \implies \sin(3 \theta) = 0\]
What this means is that we need the angle such that the sine of 3 times it is zero. To begin with sin(\theta) is zero when? Answer: when
\[\theta = n \pi\]
For some integer:
\[n = 0, \pm 1, \pm 2, ...\]
Therefore if we have sin(3 theta) then we need that:
\[3 \theta = n \pi \implies \theta = \frac{n \pi}{3}; n = 0, \pm 1, \pm 2,...\]

Answer 4

I'm a little confused about what my answer is? So I plug in 0 for n into the last equation you have.. or what? @malevolence19

Answer 5

It's all those values. Would you not agree that:
\[\sin(3 * \frac{0 \pi }{3})=\sin(3 * \frac{\pi}{3})=\sin(3 * \frac{2 \pi}{3}) = 0?\]

Answer 6

you can type
https://www.google.com/search?client=safari&rls=en&q=plot+0.5*sin(3x)&ie=UTF-8&oe=UTF-8
into google for a graph

Answer 7

it crosses the x-axis an infinite number of times, at all those places listed in mal's post

Answer 8

So what would be the standard form for an answer for this question?

Answer 9

to wit:
\[\frac{n \pi}{3}; n = 0, \pm 1, \pm 2, ...\]

Answer 10

unless they specify some interval such as between 0 and 2pi

Answer 11

So the points of intersection with the x axis is npi/3 where n=0,+/-2, +/-2... ?

Answer 12

yes

Answer 13

Ok, thanks, I find it strange that my book speaks nothing of this... or i'm blind.. but thanks!

Answer 14

I am sure they mention it somewheres...