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 $r = 1 + 5 \cos 2 \theta$ ? Note that a maximum $r$-value occurs at a point that is the maximum distance from the pole.
A) $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
B) $0 , \pi$
C) $0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$
D) $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$

Quizplus · Accepted Answer

To find the maximum $r$-values for the polar equation $r = 1 + 5\cos 2\theta$, we need to maximize the cosine function. The cosine function $\cos 2\theta$ reaches its maximum value of 1 when $2\theta = 0$ or $2\theta = \pi$, which corresponds to $\theta = 0$ or $\theta = \frac{\pi}{2}$. However, since the equation involves $2\theta$, the correct adjustments for the intervals given are $\theta = 0$ and $\theta = \pi$, where the cosine function will again be 1, leading to the maximum value of $r$.

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

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