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

question 306

Multiple Choice

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

• A) \(\theta = \frac { \pi } { 3 } + 2 k \pi , \theta = \frac { \pi } { 9 } + 2 k \pi\)
• 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:

Point Estimate

A single value given as an estimate of a population parameter, often derived from sample data.

Population Parameter

A numerical value that characterizes a given population, such as mean or standard deviation.

Sample Statistic

A numerical measure calculated from a sample data set used to estimate characteristics of the population from which it is drawn.

Unbiased Estimator

A statistical estimator that, on average, accurately estimates the parameter of interest.