Find all points of intersection (r,θ) of the curves r=2cos(θ), r=4sin(θ).

[RaiderRed]

Find all points of intersection (r,θ)(r,θ) of the curves r=2cos(θ), r=4sin(θ)r=2cos⁡(θ), r=4sin⁡(θ).

Note: In this problem the curves intersect at the pole and one other point. Only enter the answer for nonzero r in the form (r,θ)(r,θ) with θθ measured in radians.

Point of intersection = (4/sqrt5, atan(1/2))

Next find the area in closed in the intersection of the two graphs.

AREA= ????????

Many tutors have tried to help and I still struggle on this one.

 

[Dr.Peterson]

The first thing you need to do is to proofread! You pasted the problem in a way that duplicated every set of symbols. I'll make it readable here:

Find all points of intersection (r,θ) of the curves r=2cos⁡(θ), r=4sin⁡(θ).

Note: In this problem the curves intersect at the pole and one other point. Only enter the answer for nonzero r in the form (r,θ) with θ measured in radians.

Point of intersection = (4/sqrt5, atan(1/2))

Next find the area enclosed in the intersection of the two graphs.

AREA= ????????

Many tutors have tried to help and I still struggle on this one.

As I understand it, everything in bold is the problem (though I had to correct a typo), and the rest you have written, including the answer to the first part, the point of intersection. That looks correct.

Now, please tell us what you have tried to find the area.

 

[RaiderRed]

I have set up integrals etc. but I can not get the answer. I got 6, -6, 6.884, -2,014 nothing is right.

 

[Steven G]

RR, If you show us your work, then we can help you solve your problem.
Please post back showing your work.