Show that the graph ofr = 3 costi + 3 sin t j + 3 sin tkis an ellipse, and find the

Chapter 12, Problem 42

(choose chapter or problem)

Focus on Concepts

Show that the graph of

           \(\mathbf{r}=3 \cos t \mathbf{i}+3 \sin t \mathbf{j}+3 \sin t \mathbf{k}\)

is an ellipse, and find the lengths of the major and minor axes.

[Hint: Show that the graph lies on both a circular cylinder and a plane and use the result in Exercise 44 of Section 10.4.]

Equation Transcription:

𝐫𝐢𝐣𝐤

Text Transcription:

r=3 cos ti+ 3 sin tj+3 sin tk