Select the Graph of the Polar Equation Using Symmetry, Zeros $r = 4 \sin 3 \theta$

question 67

Multiple Choice

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
$r = 4 \sin 3 \theta$

• A)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \end{array}\)
• B)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \end{array}\)
• C)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \end{array}\)
• D)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \end{array}\)
• E)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \end{array}\)

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Definitions:

T-statistics

A measure used in statistical analysis to determine the difference between a sample statistic and its hypothesized population parameter, scaled by the standard error.

Within-group Variability

Refers to variations in observations within individual groups or categories in a dataset.

Null Hypothesis

The hypothesis that assumes no significant difference or relationship exists between specified populations or parameters.

Sample Size

The number of observations or data points that are collected from a subset of a larger population for the purposes of statistical analysis.