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? A.) y=sin (8(x-pi/2)) B.) 8sin(4(x-pi/2)) C.) 6sin (8(x…

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asked Aug 11, 2019 189k views

2 Answers

Jdscolam · Answer 1 · 2019-08-17T18:48:07+0000

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

$B=(2\pi)/(Current\, period)=(2\pi)/(\pi/4)=8$

Vertical shift
D= 0

Horizontal Shift
$C= \pi/2$

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

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