Sketch the curve r = 1 + sin theta. Instead of plotting points, we first sketch

Question

Sketch the curve r = 1 + sin theta. Instead of plotting points, we first sketch the graph of r = 1 + sin theta in Cartesian coordinates in the top figure by shifting the sine curve up one unit. This enables us to read at a glance the values of r that correspond to increasing values of theta. For instance, we see that as theta increases from 0 to pi/2. r (the distance from O) increases from to .so we sketch the corresponding part of the polar curve in figure As theta Increases from pi/2 to pi, the top figure shows that r decreases from to, so we sketch the next part of the curve as in figure (b). As theta increases from pi to 3pi/2, r decreases from to at shown in part. Finally, as theta increases from 3pi/2 to 2pi, r increases from to as shown In part If we let theta Increase beyond 2 pi or decrease beyond 0. we would simply retrace our path. Putting together the parts of the curve from figures (a)-(d), we sketch the complete curve In part It is called a cardioid because It's shaped like a heart.

Explanation / Answer

Given in the same order as the blanks:

r increases from 1 to 2

r decreases from 2 to 1

r decreases from 1 to 0

r increases from 0 to 1

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.