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


A) Symmetric with respect to θ=π2\theta = \frac { \pi } { 2 } ∣r∣=4 when θ=π6,π2,5π6,11π6r=0 when θ=0,π3,2π3\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} 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}
B) Symmetric with respect to θ=π2\theta = \frac { \pi } { 2 } ∣r∣=4 when θ=π6,π2,5π6,11π6r=0 when θ=0,π3,2π3\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} 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}
C) Symmetric with respect to θ=π2\theta = \frac { \pi } { 2 } ∣r∣=4 when θ=π6,π2,5π6,11π6r=0 when θ=0,π3,2π3\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} 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}
D) Symmetric with respect to θ=π2\theta = \frac { \pi } { 2 } ∣r∣=4 when θ=π6,π2,5π6,11π6r=0 when θ=0,π3,2π3\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} 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}
E) Symmetric with respect to θ=π2\theta = \frac { \pi } { 2 } ∣r∣=4 when θ=π6,π2,5π6,11π6r=0 when θ=0,π3,2π3\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} 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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