a polar function is given by r = f(θ) = 3 sin(πθ)+6. as θ increases on the interval 0 < θ < 0.5, which of…

a polar function is given by r = f(θ) = 3 sin(πθ)+6. as θ increases on the interval 0 < θ < 0.5, which of the following is true about the points of the graph of r = f(θ)? answer attempt 1 out of 2 the points are positive because they lie above the r - axis on the xy - plane polar plane and are because on the the graph is. as a result, the points on the graph are getting the origin. submit answer

a polar function is given by r = f(θ) = 3 sin(πθ)+6. as θ increases on the interval 0 < θ < 0.5, which of the following is true about the points of the graph of r = f(θ)? answer attempt 1 out of 2 the points are positive because they lie above the r - axis on the xy - plane polar plane and are because on the the graph is. as a result, the points on the graph are getting the origin. submit answer

Answer

Explanation:

Step1: Analyze the range of $\theta$

Given $0 < \theta<0.5$. Then $0<\pi\theta < 0.5\pi$.

Step2: Analyze the sine - function value

For $y = \sin x$, when $0 < x<0.5\pi$, $\sin x>0$. So, for $r = 3\sin(\pi\theta)+6$, since $\sin(\pi\theta)>0$ in the given range of $\theta$, then $r=3\sin(\pi\theta)+6>0$. In polar coordinates, when $r > 0$, the points are positive and lie in the polar - plane. Also, as $\theta$ increases from $0$ to $0.5$, $\sin(\pi\theta)$ increases from $0$ to $1$, and $r = 3\sin(\pi\theta)+6$ increases from $6$ to $9$, so the points on the graph are getting farther from the origin.

Answer:

The points are positive because they lie in the polar - plane and are increasing in value because on the given interval the graph is increasing. As a result, the points on the graph are getting farther from the origin.