# Sketch one cycle of each sine curve. Assume a > 0. Write an equation for each graph. amplitude = 2 period = (pi/2)

Sketch one cycle of each sine curve. Assume $a>0$. Write an equation for each graph. amplitude = 2 period = $\frac{\pi }{2}$

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1:
Sinusoidal Function
$y=A\mathrm{sin}\left(Bx\right)$
where $|A|=$Amplitude
A and B= Cycles from 0 to $2\pi$
period $=\frac{2\pi }{B}$
2:
Here Amplitude =2 and period= $\frac{\pi }{2}$
i.e A=2
$B=\frac{2\pi }{period}=\frac{2\pi }{\frac{\pi }{2}}=4$
The required sine curve is $y=2\mathrm{sin}\left(4x\right)$
Graph Could Be Drawn If Required