What is the extreme sin^2(θ) ?

The extreme sin^2(θ) is Minimum(pin,0),Maximum(pi/2+pin,1)

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extreme sin^2(θ)

extreme points

sin^{2} (θ)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 1)

Solution steps

Find the critical points:

θ = πn, θ = \frac{π}{2} + πn

Domain of

sin^{2} (θ) : - \infty < θ < \infty

Find intervals:

Increasing

: πn < θ < \frac{π}{2} + πn,

Decreasing

: \frac{π}{2} + πn < θ < π + πn

Plug the extreme point

x = πn

into

sin^{2} (θ) \Rightarrow y = 0

Minimum (πn, 0)

Plug the extreme point

x = \frac{π}{2} + πn

into

sin^{2} (θ) \Rightarrow y = 1

Maximum (\frac{π}{2} + πn, 1)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 1)

What is the extreme sin^2(θ) ?
The extreme sin^2(θ) is Minimum(pin,0),Maximum(pi/2+pin,1)