18. the figure shows the graph of the polar function r = g(θ), where g(θ)=3sin(3θ) in the polar coordinate…

18. the figure shows the graph of the polar function r = g(θ), where g(θ)=3sin(3θ) in the polar coordinate system for 0≤θ≤2π. there are four points labeled a, b, c, d. if the domain of g is restricted to π/2≤θ≤2π/3 which of the following describes the portion of the given graph? a) the top portion of the graph in quadrant ii from d to b b) the bottom portion of the graph in quadrant ii from b to d c) the portion of the graph in quadrant iii from d to c d) the portion of the graph in quadrant iv from c to d 19.

18. the figure shows the graph of the polar function r = g(θ), where g(θ)=3sin(3θ) in the polar coordinate system for 0≤θ≤2π. there are four points labeled a, b, c, d. if the domain of g is restricted to π/2≤θ≤2π/3 which of the following describes the portion of the given graph? a) the top portion of the graph in quadrant ii from d to b b) the bottom portion of the graph in quadrant ii from b to d c) the portion of the graph in quadrant iii from d to c d) the portion of the graph in quadrant iv from c to d 19.

Answer

Explanation:

Step1: Analyze the range of $\theta$

We know that $\frac{\pi}{2}\leq\theta\leq\frac{2\pi}{3}$. In the polar - coordinate system, $\theta=\frac{\pi}{2}$ corresponds to the positive $y$ - axis and $\theta = \frac{2\pi}{3}$ is in the second quadrant.

Step2: Determine the quadrant

Since $\frac{\pi}{2}\leq\theta\leq\frac{2\pi}{3}$, the values of $\theta$ lie in the second quadrant.

Step3: Identify the portion of the graph

As $\theta$ increases from $\frac{\pi}{2}$ to $\frac{2\pi}{3}$, moving counter - clockwise in the polar coordinate system, we move from point $B$ to point $D$ in the second quadrant.

Answer:

c) The portion of the graph in Quadrant II from B to D