What is the extreme f(x)=sin(θ) ?

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

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extreme f(x)=sin(θ)

extreme points

f (x) = sin (θ)

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

Solution steps

Find the critical points:

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Domain of

sin (θ) : - \infty < θ < \infty

Find intervals:

Increasing

: 2 πn \leq θ < \frac{π}{2} + 2 πn,

Decreasing

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

Increasing

: \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

sin (θ) \Rightarrow y = 1

Maximum (\frac{π}{2} + 2 πn, 1)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

sin (θ) \Rightarrow y = - 1

Minimum (\frac{3 π}{2} + 2 πn, - 1)

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

f (x, y) = x^{2} + 4 y^{2} - 2 ln (x y)

f (x) = - x^{3} + 2 x^{2} + 1, - 1 \leq x \leq 1

f (x) = \frac{1}{4} x^{2} + x^{3} - 2

f (x) = x^{3} - x^{2} - x + 3

f (x) = x^{3} - x^{2} - x + 4

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