Question

Write the equation of the cosine curve that has a y-intercept of (0, 4) and zeros at π and 3π.

Answer 1

The general form of cosine curve is:

`\begin{gathered} y=A\cos (Bx) \\ \text{Where:} \\ \text{A is the amplitude} \\ B\text{ is the frequency} \end{gathered}`

From the question, we were given (0,4) shows that the cosine curve has an amplitude of 4, so A=4

To get the frequency (B):

`\begin{gathered} f=\frac{2\pi}{\text{period}} \\ \text{period}=4\pi \\ f=(2\pi)/(4\pi) \\ f=(1)/(2)=B \end{gathered}`

So, therefore, the equation of the cosine curve is:

`y=4\cos ((1)/(2)x)`