Chapter 9: Polar Coordinates, Vectors

Static Equilibrium A weight of 1000 pounds is suspended from two cables as shown in the figure. What are the tensions in the two cables?

In converting from polar coordinates to rectangular coordinates, what formulas will you use?

Explain how you proceed to convert from rectangular coordinates to polar coordinates.

Show that the graph of the equation $r=-2a\cos \theta$, $a>0$

is a circle of radius a with center at $(-a,0)$in rectangular

coordinates.

Static Equilibrium A weight of 800 pounds is suspended from two cables, as shown in the figure. What are the tensions in the two cables?

Static Equilibrium A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 150 pounds, how much tension is in each part of the rope?

Is the street system in your town based on a rectangular coordinate system, a polar coordinate system, or some other system? Explain.

Explain why the following test for symmetry is valid: Replace r by -r and $\theta by-\theta$in a polar equation. If an equivalent

equation results, the graph is symmetric with respect to the

line $\theta =\frac{\mathrm{\pi }}{2}$(y-axis).

(a) Show that the test on page 574 fails for $r^2=\cos \theta$, yet this new test works.

(b) Show that the test on page 574 works for $r^2=\sin \theta$, yet

this new test fails.

Write down two different tests for symmetry with respect to

the polar axis. Find examples in which one test works and

the other fails. Which test do you prefer to use? Justify your

answer.

Static Equilibrium Repeat Problem 87 if the angle on the left is $3.8°$, the angle on the right is $2.6°$, and the weight of the tightrope walker is 135 pounds.