What is the inflection sin^2(θ) ?

The inflection sin^2(θ) is (pi/4+pin, 1/2),((3pi)/4+pin, 1/2)

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inflection sin^2(θ)

inflection points

sin^{2} (θ)

(\frac{π}{4} + πn, \frac{1}{2}), (\frac{3 π}{4} + πn, \frac{1}{2})

Solution steps

Find where

f^{''} (θ)

is equal to zero or undefined

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

Identify inflection points not in domain or where

f (θ)

is not continuous

Domain of

sin^{2} (θ) : - \infty < θ < \infty

All inflection points are in domain and not on domain edges

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

Find intervals:

Concave Upward

: πn \leq θ < \frac{π}{4} + πn,

Concave Downward

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

Concave Upward

: \frac{3 π}{4} + πn < θ < π + πn

Plug

θ = \frac{π}{4} + πn

into

sin^{2} (θ) : \frac{1}{2}

(\frac{π}{4} + πn, \frac{1}{2})

Plug

θ = \frac{3 π}{4} + πn

into

sin^{2} (θ) : \frac{1}{2}

(\frac{3 π}{4} + πn, \frac{1}{2})

(\frac{π}{4} + πn, \frac{1}{2}), (\frac{3 π}{4} + πn, \frac{1}{2})

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

f (x) = ln (x) \cdot e^{x}

- 2 x + 3 y = - 6

19 x + \frac{1}{x}

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

What is the inflection sin^2(θ) ?
The inflection sin^2(θ) is (pi/4+pin, 1/2),((3pi)/4+pin, 1/2)