ANSWERS
• Equation: ,y = 4 sin(8x)
,• Graph (1 cycle):
EXPLANATION
In the form of the equation of a sine function,
[tex]y=a\sin(b\theta)[/tex]The coefficient a is the amplitude of the curve and b is related to the period as follows,
[tex]period=\frac{2\pi}{b}[/tex]We know that the amplitude is 4, so a = 4. If the period is π/4,
[tex]\frac{\pi}{4}=\frac{2\pi}{b}[/tex]Solving for b,
[tex]b=2\pi\cdot\frac{4}{\pi}=8[/tex]Hence, the equation is y = 4 sin(8x).
