Question

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Given the equation y = 4 sin 3 2- 19.) + 9T 2 +7 The amplitude is: Preview The period is: Preview The horizontal shift is: Preview units to th Select an answer Left The midline is: y = Preview Right

Answer 1

The general equation of a sine function is

y = A sin (B(x - C)) + D

where

A is the amplitude

$2\pi / B \, \, is \, the \, period$

C is the horizontal shift

D is the vertical translations / midline

In this case,

$y = 4\, sin (\frac{3\pi}{4}x - \frac{9\pi}{2}) + 7$

=> $y = 4\, sin (\frac{3\pi}{4}(x - 6)) + 7$

Therefore,

A = 4

B = $3\pi / 4$

C = 6

D = 7

Amplitude = A = 4

Period = $2\pi / (3\pi / 4)$ = 8 / 3

Horizontal shift is 6 units to the right

The midline is: y = 7