What is the extreme sin(θ)-sqrt(3)cos(θ) ?

The extreme sin(θ)-sqrt(3)cos(θ) is Maximum((5pi)/6+2pin,2),Minimum((11pi)/6+2pin,-2)

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extreme sin(θ)-sqrt(3)cos(θ)

extreme points

sin (θ) - 3 cos (θ)

Maximum (\frac{5 π}{6} + 2 πn, 2), Minimum (\frac{11 π}{6} + 2 πn, - 2)

Solution steps

Find the critical points:

θ = \frac{5 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Domain of

sin (θ) - 3 cos (θ) : - \infty < θ < \infty

Find intervals:

Increasing

: 2 πn \leq θ < \frac{5 π}{6} + 2 πn,

Decreasing

: \frac{5 π}{6} + 2 πn < θ < \frac{11 π}{6} + 2 πn,

Increasing

: \frac{11 π}{6} + 2 πn < θ < 2 π + 2 πn

Plug the extreme point

x = \frac{5 π}{6} + 2 πn

into

sin (θ) - 3 cos (θ) \Rightarrow y = 2

Maximum (\frac{5 π}{6} + 2 πn, 2)

Plug the extreme point

x = \frac{11 π}{6} + 2 πn

into

sin (θ) - 3 cos (θ) \Rightarrow y = - 2

Minimum (\frac{11 π}{6} + 2 πn, - 2)

Maximum (\frac{5 π}{6} + 2 πn, 2), Minimum (\frac{11 π}{6} + 2 πn, - 2)

f (x, y) = (- x^{2} - y^{2} + 2 y - 1)

f (x, y) = 7 (\frac{1}{5} (y + 3) e^{- x y})

y = 5 x^{2} - 15 x + 3

f (x, y) = x (e^{x} - e^{y})

f (x) = 9 x^{2} - 27 x + 6

What is the extreme sin(θ)-sqrt(3)cos(θ) ?
The extreme sin(θ)-sqrt(3)cos(θ) is Maximum((5pi)/6+2pin,2),Minimum((11pi)/6+2pin,-2)