What is the extreme (sin(5x))/(sin^5(x)) ?

The extreme (sin(5x))/(sin^5(x)) is Minimum(pi/4+pin,-4),Maximum(pi/2+pin,1),Minimum((3pi)/4+pin,-4)

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extreme (sin(5x))/(sin^5(x))

extreme

Minimum (\frac{π}{4} + πn, - 4), Maximum (\frac{π}{2} + πn, 1), Minimum (\frac{3 π}{4} + πn, - 4)

Solution steps

Find the critical points:

x = \frac{π}{4} + πn, x = \frac{π}{2} + πn, x = \frac{3 π}{4} + πn

Domain of

\frac{sin ( 5 x )}{sin ^{5} ( x )} : πn < x < π + πn

Find intervals:

Decreasing

: πn < x < \frac{π}{4} + πn,

Increasing

: \frac{π}{4} + πn < x < \frac{π}{2} + πn,

Decreasing

: \frac{π}{2} + πn < x < \frac{3 π}{4} + πn,

Increasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

\frac{sin ( 5 x )}{sin ^{5} ( x )} \Rightarrow y = - 4

Minimum (\frac{π}{4} + πn, - 4)

Plug the extreme point

x = \frac{π}{2} + πn

into

\frac{sin ( 5 x )}{sin ^{5} ( x )} \Rightarrow y = 1

Maximum (\frac{π}{2} + πn, 1)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

\frac{sin ( 5 x )}{sin ^{5} ( x )} \Rightarrow y = - 4

Minimum (\frac{3 π}{4} + πn, - 4)

Minimum (\frac{π}{4} + πn, - 4), Maximum (\frac{π}{2} + πn, 1), Minimum (\frac{3 π}{4} + πn, - 4)

What is the extreme (sin(5x))/(sin^5(x)) ?
The extreme (sin(5x))/(sin^5(x)) is Minimum(pi/4+pin,-4),Maximum(pi/2+pin,1),Minimum((3pi)/4+pin,-4)