Period of sin wave = 1/2
Period of parent sine function is 2π.
This means the x value of sine function (sin(x)) has to be divided by 4π to get a period of 1/2 because 2π/4π = 1/2
Thus, our function will be of the form: [tex]sin( \frac{x}{4 \pi }) [/tex]
Maximum Value = 10
Minimum Value = -4
Amplitude of the function = (Maximum Value - Minimum Value)/2
So, amplitude of the function is 7
Thus, the function will be of the form:
[tex]7sin( \frac{x}{4 \pi } )[/tex]
The function has a y-intercept other than zero, this means the function will be of the form:
[tex]y=7sin( \frac{x}{4 \pi } )+k[/tex]
The y-intercept is 3. This means for x=0, y=3. Using the values, we get:
[tex]3=7sin(0)+k \\ \\
3=k[/tex]
Thus the equation of the sinusoidal function becomes:
[tex]y=7sin( \frac{x}{4 \pi } )+3[/tex]
