Answer
Fill the blanks with
$|a|, \displaystyle \ \ \frac{2\pi}{k}, \ \ b,$
$4, \displaystyle \ \ \frac{2\pi}{3}, \ \ \frac{\pi}{6}.$
Work Step by Step
See:
Graphs of Transformations of Sine and Cosine (p. 424)
For
$y=a\sin k(x-b)$, $(k>0),\qquad$
$y=a\cos k(x-b)$, $(k>0)$
Amplitude: $|a|$,
Period: $\displaystyle \frac{2\pi}{k}$,
Horizontal shift: $b$
An appropriate interval on which to graph one complete period is $[b, b+(2\pi/k)]$
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The first three blanks: $|a|, \displaystyle \ \ \frac{2\pi}{k}, \ \ b.$
For $y=4\displaystyle \sin 3(x-\frac{\pi}{6})$, a=4, k=3, $b=\displaystyle \frac{\pi}{6}.$
Amplitude: $|a|=4$,
Period: $\displaystyle \frac{2\pi}{k}=\frac{2\pi}{3}$,
Horizontal shift: $b =\displaystyle \frac{\pi}{6}$
Fill the remaining blanks with
$4, \displaystyle \ \ \frac{2\pi}{3}, \ \ \frac{\pi}{6}.$