What is the extreme f(x)=sin(2θ) ?

The extreme f(x)=sin(2θ) is Maximum(pi/4+pin,1),Minimum((3pi)/4+pin,-1)

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extreme f(x)=sin(2θ)

extreme

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

Solution steps

Find the critical points:

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Domain of

sin (2 θ) : - \infty < θ < \infty

Find intervals:

Increasing

: πn \leq θ < \frac{π}{4} + πn,

Decreasing

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

Increasing

: \frac{3 π}{4} + πn < θ < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

sin (2 θ) \Rightarrow y = 1

Maximum (\frac{π}{4} + πn, 1)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

sin (2 θ) \Rightarrow y = - 1

Minimum (\frac{3 π}{4} + πn, - 1)

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

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