Question

y=-6sin4theta has amplitude of?

Answer 1

What's the coefficient of the sine function here?

Take the absolute value of that coeffici8ent and you'll then have the amplitude.

Answer 2

Generally, a sine function is written as \[y=a \sin (bx + c),\]

where the "amplitude" is |a|, the frequency is b and the phase shift depends upon the value of c.

Given y=-6 sin 4 theta,

the amplitude is |-6|; the period is \[\frac{ 2 \pi }{ b }=\frac{ 2 \pi }{ 4 }=\frac{ \pi }{ 2 },\]

Answer 3

and the phase shift is -c/b, or, here, -0/4 = 0.