Solve the problem.
-For what values of $\theta ( 0 \leq \theta

Question

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) $\frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 }$

Quizplus · Accepted Answer

The maximum r-values occur when $\sin 3 \theta = -1$, which occurs when $3 \theta = \frac { 3 \pi } { 2 } + 2 \pi k$ for any integer $k$. Solving for $\theta$, we get $\theta = \frac { \pi } { 2 } + \frac { 2 \pi k } { 3 }$. Since $0 \leq \theta < 2 \pi$, the only values of $k$ that give valid solutions are $k = 0, 1, 2$, which give $\theta = \frac { \pi } { 2 }, \frac { 7 \pi } { 6 }, \frac { 11 \pi } { 6 }$.

Solve the Problem θ(0≤θ<2π)\theta ( 0 \leq \theta < 2 \pi )θ(0≤θ<2π)

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