Select the Graph of the Polar Equation Using Symmetry, Zeros $r = 4 \sin ( 2 \theta )$

question 104

Multiple Choice

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
$r = 4 \sin ( 2 \theta )$

• A)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) , the polar axis, and the pole \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi \end{array}\)
• B)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) , the polar axis, and the pole \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi \end{array}\)
• C)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) , the polar axis, and the pole \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi \end{array}\)
• D)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) , the polar axis, and the pole \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi \end{array}\)
• E)Symmetric with respect to \(\theta = \frac { \pi } { 2 }\) , the polar axis, and the pole \(\begin{array} { c } | r | = 4 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \\ r = 0 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi \end{array}\)

---

Definitions:

Waist-To-Hip Ratio

A measurement used to assess the distribution of body fat by comparing the circumference of the waist to that of the hips.

Body Fat

The portion of the human body composed of fat cells, which serve as energy storage and insulation, and play important roles in hormone regulation.

Dietary Fat

A macronutrient found in food items, essential for various bodily functions but often monitored for healthy dieting.

Sugar Consumption

The intake or consumption of sweet-tasting, soluble carbohydrates, which can influence health outcomes.