Find the Solutions of the Equation That Are in the Interval

question 10

Multiple Choice

Find the solutions of the equation that are in the interval $[ 0,2 \pi ) .$ $\cot ^ { 2 } u \cos u = \cos u$

• A) \(\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• B) \(0 , \pi , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }\)
• C) \(0 , \pi , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• D) \(\frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• E) no solution

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Definitions:

Hybrid Atomic Orbitals

Orbitals formed by the mixing of atomic orbitals in an atom, leading to equivalent orbital shapes suited for bonding.

C-C σ Bond

A single bond formed between two carbon atoms due to the overlap of sp3 hybrid orbitals.

Acetaldehyde

An organic chemical compound with the formula CH3CHO, known as the simplest aldehyde after formaldehyde, used in various industrial processes.

CCN Bond Angle

Refers to the angle formed between two carbon atoms and a nitrogen atom in certain molecular structures.