Question

We are given the polar equation r = cos(4θ).

If 0 < θ < π and r = 0, then

θ =?

Answer 1

if r is 0 then there is no radius if there's no radius there's no circle. I think something's missing from the problem.

Answer 2

the graph is a rose and is symmetrical on x and y axis. So when r=0 theta would not be there?

Answer 3

cos(90)=0
so,4θ=90
θ=22.5= π /8

Answer 4

there is more than one theta, there are four

Answer 5

So basically we have\[0=\cos(4\theta)\] which means \[4\theta=(n+1/2)*\pi\]where n is an integer. However \[0<\theta<\pi\] which means that\[\theta=\pi/8\]

Answer 6

so I am right

Answer 7

Actually I lied there are more solutions. Just a sec.

Answer 8

where did you get 4theta=(n+1/2)*pi from?

Answer 9

you can multiply by n where n=1,2,3...8

Answer 10

\[\Theta=(n+1/2)*\pi/4\]
So the solutions are:\[\Theta=\pi/8, 3\pi/8, 5\pi/8, 7\pi/8\]

Answer 11

I got that from the fact that cos((n+1/2)*pi)=0. Just like sin(npi)=0.

Answer 12

cos(pi/2)=cos(3pi/2)=cos(5pi/2)=...=0

Answer 13

ok, that makes sense but why would you set 4theta to 0 instead of cos(4theta)?

Answer 14

I didn't. I set 4theta to the value which makes cos(4theta)=0.

Answer 15

I understand that but why?

Answer 16

cos(90)=0
so,4θ=90
θ=22.5= π /8

Answer 17

Because cos(4theta)=r=0

Answer 18

ok

Answer 19

Does that all make sense? Trig functions get tricky because you have to be very careful that you operate within the given domain and don't miss any solutions.

Answer 20

kind of, I understand trig part but the reason why the solution is taken like that is confusing.

Answer 21

Can I explain something better? Which part specifically is confusing?

Answer 22

the answer θ=22.5= π /8

Answer 23

why cant you use tantheta=y/x and solve for x and y based on the r given. so, x=rcostheta and y=rsintheta. then solve for theta?

Answer 24

Well you are given r=0 and you aren't given information about cartesian coordinates so I would recommend doing it in polar coordinates.

Answer 25

Think of it like solving the equation y=sinx and they tell you y=0. What do you do? You solve it similarly: x=npi. And then you would worry about the domain for x.

Answer 26

ok I think I understand, thanks

Answer 27

Ok good luck with your studies. ;p

Answer 28

sorry i answered that quite tired, basically what i meant was that if r=0 theta would equal 0 so you need to find the answers of theta that would allow the cos function go to 0. 0=Cos (theta) values theta pi/2 and 3pi/2 but since there is no radius it is simply the axis and you're at the origin, but you still need those values in order the trace the rose curve. Hopefully that helps a bit more. =)