Question

which rectangular equation is equivalent to the polar equation r csc theta=8

A. y=8
B. x^2+(y-4)^2=16
C. x=8y^2
D. x=8

Answer 1

No idea i think the option is B

Answer 2

do you know what csc(theta) is?

Answer 3

1/sin theta?

Answer 4

good. so your equation is:\[\frac{r}{\sin(\theta)}=8\]so, first multiply both sides by \(\sin(\theta)\) - what do you end up with?

Answer 5

r=8sintheta

Answer 6

great! now the next "trick" to notice is that if you now multiply both sides by "r" you should get some familiar terms - what do you get?

Answer 7

8sintheta(r) ?

Answer 8

both sides

Answer 9

8sinthetar=8sintheta r ? like that?

Answer 10

no, you currently have:

r = 8sin(theta)

now multiply both sides of this equation by r - what will you end up with?

Answer 11

thats why doesnt the r cancel out and moves to the other side of the euqation. 8sin(theta)r

Answer 12

we are "multiplying" not dividing - so the "r" should not cancel out

Answer 13

so its r^2?

Answer 14

yes - that is what you get on the left-hand-side of the equals sign, and what about the right-hand-side?

Answer 15

r^2=8 sin(theta)r

Answer 16

great! this is usually written as:\[r^2=8r\sin(\theta)\]now, can you spot what to do next?

Answer 17

square root both sides to cancel out the squared?