Find the Largest Interval on Which the Function $f ( \theta ) = \cos ^ { 2 } \theta$

question 186

Essay

Find the largest interval on which the function $f ( \theta ) = \cos ^ { 2 } \theta$ is concave upward.

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Definitions:

Sample Size

The count of data points or observations gathered in a subset from a larger group.

Randomized Design

An experimental setup where subjects or experimental units are randomly allocated to different groups or treatments.

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution, typically in the context of parameter estimation or hypothesis testing.

Observations

The act of systematically viewing and recording phenomena or data to gather information about the world.