Solve the problem.
-What is the maximum $\mathrm { r }$-value for the polar equation $r = - 1 + 6 \sin \theta$ ? Note that a maximum $r$-value is a maximum value of $| \mathrm { r } |$, the maximum distance from the pole.
A) 5
B) 6
C) 7
D) 1

Question

Quizplus · Accepted Answer

The maximum $r$-value occurs when $\sin \theta = 1$, which gives $r = -1 + 6(1) = 5$. However, since we're looking for the maximum $|r|$, and $r$ can also be negative, we consider the case when $\sin \theta = -1$, giving $r = -1 + 6(-1) = -7$. Thus, the maximum $|r|$ is 7.

Solve the Problem r\mathrm { r }r -Value for the Polar Equation

Solve the Problem $\mathrm { r }$ -Value for the Polar Equation