A wave is modeled with the function y = 1/2 sin 3 theta. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

Question

anonymous · Answer

$$y = \frac{ 1 }{ 2 } \sin 3 \theta $$

anonymous · Answer

if someone can help me figure out how to graph it, i can find the period, amplitude, and points of intersection with the x-axis myself.

anonymous · Answer

the amplitude is $\frac{1}{2}$ because of the coefficient out front

anonymous · Answer

hope this is clear, since $\sin(x)$ goes from $-1$ to $1$ this means $\frac{1}{2}\sin(x)$ goes from $-\frac{1}{2}$ to $\frac{1}{2}$

anonymous · Answer

as for the period, the period of $\sin(bx)$ is $\frac{2\pi}{b}$ 
in this case the period will therefore be $\frac{2\pi}{3}$

anonymous · Answer

you can solve for the $x$ intercepts, by setting the various zeros of $\sin(x)$ equal to $3x$
for example 
$$3x=0\iff x=0$$
$$3x=\pi\iff x=\frac{\pi}{3}$$
$$3x=2\pi\iff x=\frac{2\pi}{3}$$ and so on

anonymous · Answer

as for a graph, i would use this http://www.wolframalpha.com/input/?i=1%2F+2*sin%283x%29

anonymous · Answer

I found some of the answers myself (finally figured it out!)
I had these:

Amplitude: 1/2
Period: 2pi/3
Intersections: Infinitely many, but pi/3, 2pi/3, so on and so forth. Hopefully those were right.

anonymous · Answer

From what you said, they look okay.

anonymous · Answer

yes, you are correct

anonymous · Answer

Awesome! Thanks for your help.

anonymous · Answer

yw

anonymous · Answer

@satellite73 i don't get it :C

anonymous · Answer

how you get b