How do you graph and list the amplitude, period, phase shift for $y = - 3 cos (3 x) + 3$ $y=-3cos(3x)+3$ ?

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Answer 1 · 2018-02-02T02:36:49

The amplitude of the function is $3$ $3$ , the period is $\frac{2 π}{3}$ $(2pi)/3$ , and the phase shift is $0$ $0$ .

For the general $cos$ $cos$ wave

$y = A cos (B (x - C)) + D$ $y=Acos(B(x-C))+D$ ,

the wave is amplified by $| A |$ $|A|$ , horizontally compressed by $B$ $B$ , translated right $C$ $C$ (phase shift), and translated up $D$ $D$ .

Here are the values of our equation:

$y = - 3 cos (3 x) + 3$ $y=-3cos(3x)+3$

$| A | = amplitude = 3$ $|A|="amplitude"=3$

$B = compression = 3$ $B="compression"=3$

$C = phase shift = 0$ $C="phase shift"=0$

$D = vertical shift = 3$ $D="vertical shift"=3$

To find our period, we take $2 π$ $2pi$ (the period of the normal sinusoidal wave) and divide it by our B value:

$period = \frac{2 π}{B} = \frac{2 π}{3}$ $"period"=(2pi)/B=(2pi)/3$

Finally, the phase shift is our $C$ $C$ value, which in this case is $0$ $0$ (because it is not present).

How do you graph and list the amplitude, period, phase shift for y=−3cos(3x)+3y=-3cos(3x)+3?