What is the graph of $y = sin (\frac{x}{2})$ $y=sin(x/2)$ ?

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What is the graph of $y = sin (\frac{x}{2})$ $y=sin(x/2)$ ?

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Answer 1 · 2014-10-06T05:00:09

First, calculate the period.

$ω = \frac{2 π}{B} = \frac{2 π}{\frac{1}{2}} = (\frac{2 π}{1}) \cdot (\frac{2}{1}) = 4 π$ $omega=(2pi)/B=(2pi)/(1/2)=((2pi)/1)*(2/1)=4pi$

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

$\frac{4 π}{4} = π$ $(4pi)/(4)=pi$

$0, π, 2 π, 3 π, 4 π \to x$ $0,pi,2pi,3pi,4pi ->x$ -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 $4 π$ $4pi$ .
The calculator converts $4 π$ $4pi$ to its decimal equivalent.

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Press the GRAPH button.

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What is the graph of $y = sin (\frac{x}{2})$ $y=sin(x/2)$ ?

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