Find All Solutions of the Following Equation in the Interval $[ 0,2 \pi )$

question 37

Multiple Choice

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ .
$$\csc ^ { 2 } x = \cot x + 1$$

• A)
• \(x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 4 \pi } { 3 }\)
• B)
• \(x = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }\)
• C)
• \(x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }\)
• D)
• \(x = \frac { \pi } { 4 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 4 } , \frac { 3 \pi } { 2 }\)
• E)
• \(x = \frac { \pi } { 4 } , \frac { 4 \pi } { 3 } , \frac { 11 \pi } { 6 }\)

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Definitions:

First Law of Thermodynamics

This principle states that energy cannot be created or destroyed, only transformed from one form to another, implying that the total energy in an isolated system remains constant.

Concentrated Energy

Energy that is intensified or focused within a small area or volume, often for the purpose of efficient transmission or usage.

Usable Energy

Energy in a form that can be directly applied to perform work or be processed into a form suitable for human needs, such as electricity or mechanical power.

Energy Transformation

The process of converting energy from one form to another, such as kinetic energy to electrical energy, fundamental to various natural phenomena and technologies.