Question

What is the general equation of a sine function with an amplitude of 6, a period of pi/4, and a horizontal shift of pi/2?

Answer 1

The general equation of the sine function y=f(x) is defined as

$Y=AsinB(x-C)+D$

where A is the Amplitude

B represents the frequency of the function with period equals $2\pi/B$

C represents the Horizontal shift, For Phase shift= -C/B

D represents the Vertical shift.

The data given that the amplitude of the function A=6

$B=\frac{2\pi}{Current\, period}=\frac{2\pi}{\pi/4}=8$

Vertical shift $D= 0$

Horizontal Shift $C= \pi/2$

Now plug in $\neq A=6, B=8\, and \, C=\pi/2$ in the general equation of sine function, we get

$y=6\sin8(x-\pi/2)+0\\y=6\sin 8(x-\pi/2))$