Question

What is an equation for a sine curve with amplitude 2 and a period 4pi radians?

Answer 1

The equation for a sine curve with amplitude 2 and a period 4π radians is
`y=2sin\,((x)/(2))`.

Step-by-step explanation:

We have to write the Equation of Sine function with amplitude 2 and period 4π.

We know the equation of normal sine function with amplitude 1 and period 2π is as follows

y = sin(x)

We use the transformation of sine function.

To increase or decrease the amplitude we multiply the constant with normal sine function.

So, To increase the amplitude to 2

we have function , y = 2 × sin(x) = 2sin(x)

Now to have a period of 4π we divide the angle of sine function by 2

We get,

`y=2sin\,((x)/(2))`

Therefore, The equation for a sine curve with amplitude 2 and a period 4π radians is
`y=2sin\,((x)/(2))`

Answer 2

Given a normal sine function, y=sin (x), period=2pi
y=sin(x)=sin(1*x);
1 is the coefficient, i.e c, helps us to calculate for the period of the function.
period=(2pi)/c=(2pi/1)=2pi
In our case where the period is 4pi,
then;
(2pi)/c=4pi
thus;
c=1/2
Therefore our formula can be written as:
y=a sin(c*x)=sin(1/2x)
but amplitude,a=2;
therefore;
y=4sin (1/2x)