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Expert-verified Found in: Page 523 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # 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 1: Draw a Graph$${\rm{y = 2 + sin\theta }}$$. ## 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? 