What is the extreme sin(t)-(cos(t)+sin(t)) ?

The extreme sin(t)-(cos(t)+sin(t)) is Minimum(2pin,-1),Maximum(pi+2pin,1)

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extreme sin(t)-(cos(t)+sin(t))

extreme

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

Solution steps

Find the critical points:

t = 2 πn, t = π + 2 πn

Domain of

sin (t) - (cos (t) + sin (t)) : - \infty < t < \infty

Find intervals:

Increasing

: 2 πn < t < π + 2 πn,

Decreasing

: π + 2 πn < t < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

sin (t) - (cos (t) + sin (t)) \Rightarrow y = - 1

Minimum (2 πn, - 1)

Plug the extreme point

x = π + 2 πn

into

sin (t) - (cos (t) + sin (t)) \Rightarrow y = 1

Maximum (π + 2 πn, 1)

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

What is the extreme sin(t)-(cos(t)+sin(t)) ?
The extreme sin(t)-(cos(t)+sin(t)) is Minimum(2pin,-1),Maximum(pi+2pin,1)