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What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin bθ, what is an equation for the sine curve?amplitude = 4, period = 1/4 pi, and a > 0.

Sagot :

ANSWERS

• Equation: ,y = 4 sin(8x)

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• 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).

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