• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Select your language

Suggested languages for you:

Americas

Europe

Q34E

Expert-verified
Found in: Page 523

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

Answers without the blur.

Just sign up for free and you're in.

Sketch the curve with the given polar equation by first sketching the graph $${\rm{r}}$$as a function of $${\rm{\theta }}$$Cartesian coordinates.$${\rm{r = 2 + sin\theta }}$$

The Curve is drawn with a polar equation by sketching a graph.

See the step by step solution

Step 2: Draw a Graph$${\rm{r = 2 + sin\theta }}$$.

First, make a Cartesian graph $${\rm{\theta }}$$at the horizontal axis and $${\rm{r}}$$the vertical axis. This is the transformation of $${\rm{y = sinx}}$$with amplitude 1, reflected over the $${\rm{X - }}$$axis and shifted up by 2 units. Therefore, $${\rm{r}}$$will vary between 1 and 3 and complete one cycle from zero to$${\rm{2\pi }}$$.

To Plot the polar graph considers an increment of $${\rm{\pi /6}}$$approximately equal to$${\rm{0}}{\rm{.5236}}$$.

 $${\rm{\theta }}$$ $${\rm{r}}$$ 0.0000 2.0000 0.5236 2.5000 1.0472 2.8660 1.5708 3.0000 2.0944 2.8660 2.6180 2.5000 3.1416 2.0000 3.6652 1.5000 4.1888 1.1340 4.7124 1.0000 5.2360 1.1340 5.7596 1.5000 6.2832 2.0000

Thus, the curve is drawn with the polar equation.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.