Question

convert to rectangular form r=4sec theta

Answer 1

\[
r = 4 \sec (\theta)= \frac 4 {\cos(\theta)} \\

r \cos(\theta) = 4\\
x =4
\]
It is a line

Answer 2

Would you mind if I asked you more of these problems?

Answer 3

Please do

Answer 4

r^2 = 8 sec theta csc theta

Answer 5

r= 7 csc theta

r=12/ 8 csc theta + 11 sin theta

theta = - pie/3

theta = pie / 4

Answer 6

r= 8 sin theta

Answer 7

r = 7 csc(theta)
rsin(θ)=7
y=7

Answer 8

r=12/ 8 csc theta + 11 sin theta

\[r = \frac {12} 8 \frac 1{\sin(\theta)}+ 11 \sin(\theta)\\
r\sin(\theta) = \frac {12} 8 + 11 \sin^2(\theta )\\
y = \frac {12} 8 +11 \frac {x^2}{ r^2}\\
y = \frac {12} 8 +11 \frac {x^2}{ x^2+ y^2}\\
\]

Answer 9

You should be able to mimic what I did to do the rest. Try them and let me know.

Answer 10

r= 8 sin theta
did you get y= -8

Answer 11

theta = - pie/3
theta = pie / 4
I'm a bit lost on these two

Answer 12

Hey, do u by any chance know how to give 3 different polar points that are equivalent to: (0,-5)

Answer 13

r= 8 sin theta this is not y=8
try to multiply both sides by r thenn
\[
r^2= 8 r \sin(\theta)
\]
In ploar coordinates
\[
x= r \cos(\theta) \\
y= r \sin(\theta)\\
x^2+y^2 = r^2
\]
Use the above to finish the problem.

Answer 14

did you get zero for both

Answer 15

You should get
\[
x^2 + y^2 = 8 \sin(\theta)\]

Answer 16

What does it mean that the angle is constant,like
\[\theta = \frac \pi 4
\]
It means that we are on a line that makes an angle of 45 degrees with the x-axis.
What is the equation of this line?

Answer 17

Do some practice on http://moltest.missouri.edu/mucgi-bin/calculus.cgi
and choose Calculus(II) Parametric and Polar coordinates. You will be good at doing this kind of problems and more.