Question

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.

Answer 1

ANSWERS

• Equation: ,y = 4 sin(8x)

,

• Graph (1 cycle):

Step-by-step explanation

In the form of the equation of a sine function,

`y=a\sin(b\theta)`

The coefficient a is the amplitude of the curve and b is related to the period as follows,

`period=(2\pi)/(b)`

We know that the amplitude is 4, so a = 4. If the period is π/4,

`(\pi)/(4)=(2\pi)/(b)`

Solving for b,

`b=2\pi\cdot(4)/(\pi)=8`

Hence, the equation is y = 4 sin(8x).