Question

A sine function has an amplitude of 3, a period of π, and a phase shift of pi over 2 period What is the y-intercept of the function?

Answer 1

The sine fuction we have is

$f(x)=3\sin \mleft(2x+\frac{\pi}{2}\mright)$

If we want the y-intercept, we must put x = 0, then

$\begin{gathered} f(x)=3\sin (2x+\frac{\pi}{2}) \\ \\ f(0)=3\sin (\frac{\pi}{2}) \\ \\ f(0)=3\cdot1 \\ \\ f(0)=3 \end{gathered}$

Therefore the y-intercept is 3.