What is the graph of $y = sin (\frac{x}{3})$ $y=sin (x/3)$ ?

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What is the graph of $y = sin (\frac{x}{3})$ $y=sin (x/3)$ ?

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Answer 1 · 2014-10-06T04:45:44

First, calculate the period.

$ω = \frac{2 π}{B} = \frac{2 π}{\frac{1}{3}} = (\frac{2 π}{1}) \cdot (\frac{3}{1}) = 6 π$ $omega=(2pi)/B=(2pi)/(1/3)=((2pi)/1)*(3/1)=6pi$

Break up $6 π$ $6pi$ into fourth by dividing by $4$ $4$ .

$\frac{6 π}{4} = \frac{3 π}{2}$ $(6pi)/(4)=(3pi)/(2)$

$0, \frac{3 π}{2}, 3 π, \frac{9 π}{2}, 6 π \to x$ $0,(3pi)/(2),3pi,(9pi)/2,6pi ->x$ -values

These $x$ $x$ values correspond to ...

$sin (0) = 0$ $sin(0)=0$

$sin (\frac{π}{2}) = 1$ $sin((pi)/(2))=1$

$sin (π) = 0$ $sin(pi)=0$

$sin (\frac{3 π}{2}) = - 1$ $sin((3pi)/2)=-1$

$sin (2 π) = 0$ $sin(2pi)=0$

Enter the function using the Y= button

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Press the WINDOW button.
Enter the Xmin of $0$ $0$ and Xmax of $6 π$ $6pi$ .
The calculator converts $6 π$ $6pi$ to its decimal equivalent.

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Press the GRAPH button.

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