Question

Help please..
Idetify the curve by finding a cartesian equation for the curve

Answer 1

r=tan theta sec theta

Answer 2

\[\large\rm r=\tan \theta\cdot \sec \theta\]Converting to sines and cosines might help,\[\large\rm r=\frac{\sin \theta}{\cos \theta}\cdot \frac{1}{\cos \theta}\]Hmm let's multiply both sides by cosine,\[\large\rm r \cos \theta=\frac{\sin \theta}{\cos \theta}\]Hmm no, let's multiply by cosine again,\[\large\rm r \cos^2\theta=\sin \theta\]And let's multiply both sides by r,\[\large\rm r^2 \cos^2\theta=r \sin \theta\]Hmm we can rewrite the left side like this,\[\large\rm (r \cos \theta)^2=r \sin \theta\]

Answer 3

Understand what to do from that point?

Answer 4

Wait so why multiply by r on each side?

Answer 5

The main reason was because I wanted to try and create \(\rm r\sin\theta\) on the right side because we can convert that directly to Cartesian, ya?

Answer 6

Oh yeah

Answer 7

Okay how about this one theta =pi/3
Same directions

Answer 8

Ummm I think this one represents just a straight line... lemme think...

Answer 9

So we rotate an angle of pi/3.

Answer 10

Oh so theta is treated as x?

Answer 11

What values of r satisfy this line?
Well, all of them because there is no r in the equation.

Answer 12

so all positive r values