graph the polar curve r = 3 - 4 sin θ\nselect a curve and use the point(s) to adjust:\nrose\ncircle\nlimacon…

graph the polar curve r = 3 - 4 sin θ\nselect a curve and use the point(s) to adjust:\nrose\ncircle\nlimacon (inner loop)\ncardioid (hits pole)\nlimacon (no inner loop)\nline

graph the polar curve r = 3 - 4 sin θ\nselect a curve and use the point(s) to adjust:\nrose\ncircle\nlimacon (inner loop)\ncardioid (hits pole)\nlimacon (no inner loop)\nline

Answer

Explanation:

Step1: Identificar la forma de la curva polar

La ecuación de la curva polar es $r = a - b\sin\theta$, donde $a = 3$ y $b = 4$. Como $a\lt b$ ($3\lt4$), la curva es un limacón con un lazo interior.

Step2: Encontrar los valores críticos

Evaluamos $r$ en $\theta = 0,\frac{\pi}{2},\pi,\frac{3\pi}{2}$. Cuando $\theta = 0$, $r=3 - 4\sin(0)=3$. Cuando $\theta=\frac{\pi}{2}$, $r = 3-4\sin(\frac{\pi}{2})=3 - 4=- 1$. Cuando $\theta=\pi$, $r = 3-4\sin(\pi)=3$. Cuando $\theta=\frac{3\pi}{2}$, $r = 3-4\sin(\frac{3\pi}{2})=3+4 = 7$.

Answer:

La curva es un Limacón (inner loop).