Solve the Equation $$\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }$$

question 158

Multiple Choice

Solve the equation. Give a general formula for all the solutions.
- $$\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }$$

• A) \(\theta = \frac { \pi } { 3 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi\)
• B) \(\theta = \pi + 6 \mathrm { k } \pi , \theta = 2 \pi + 6 \mathrm { k } \pi\)
• C) \(\theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 18 } + 2 \mathrm { k } \pi\)
• D) \(\theta = \frac { \pi } { 2 } + 6 \mathrm { k } \pi , \theta = \pi + 6 \mathrm { k } \pi\)

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Definitions:

Model Minority

A stereotype applied to a particular demographic group suggesting that they achieve a higher degree of socioeconomic success than the population average, often oversimplifying real challenges.

Hedonism

A philosophical belief that pleasure or happiness is the highest good and ultimate aim of human life.

Altruism

The selfless concern for the well-being of others, often leading to acts of kindness or generosity without expectation of personal gain.

Egoism

A theory in ethics that treats self-interest as the foundation of morals.