Solve the Problem $\theta ( 0 \leq \theta < 2 \pi )$

question 113

Multiple Choice

Solve the problem.
-For what values of $\theta ( 0 \leq \theta < 2 \pi )$ do maximum r-values occur on the graph of the polar equation $\mathrm { r } = 3 - 4 \sin 3 \theta$ ? Note that a maximum $\mathrm { r }$ -value occurs at a point that is the maximum distance from the pole.

• A) \(\frac { \pi } { 2 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }\)
• B) \(\frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }\)
• C) \(\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }\)
• D) \(\frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 }\)

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Definitions:

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The verbal expression or communication of thoughts and feelings through the articulation of sounds.

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The ability to understand and grasp the meaning of something.

Parietal Lobes

Regions of the brain located behind the frontal lobes, involved in processing sensory information regarding the location of parts of the body as well as interpreting visual information and processing language and mathematics.

Spatial Location

The specific coordinates or position of an object or place in space.