Question

find the range of f
f(x)= 2 sin(3x)
where x is between (-pi/6) and (pi/6)

Answer 1

if \(x=-\frac{\pi}{6}\) then
\[3x=3\times (-\frac{\pi}{6})=-\frac{\pi}{2}\]

Answer 2

\[\sin(-\frac{\pi}{2})=-1\] and that is the smallest that since can be
then
\[2\sin(-\frac{\pi}{2})=2\times (-1)=-2\] and that is your minimum value for the range

Answer 3

thanks!!!

Answer 4

oops i meant to say "that is the smallest that SINE can be"

Answer 5

hint, you will find the largest value similarly if you replace \(x\) by \(\frac{\pi}{6}\)

Answer 6

yw