I missed the following 3 questions on my Cal II quiz this week. Someone please s

Question

I missed the following 3 questions on my Cal II quiz this week. Someone please show me how to work them so I can find my mistake. Show your work for a good rating.

13) Find the rectangular coordinates of the point(s) of intersection of the following polar curves. r=6sin? r=6cos?

15) Calculate the area of the given region: r=2cos?, r=2sin?, the rays ?=0 and ?=(?/4)

20) Which of the following represents the area outside r=6cos(2?) but inside r=6?

a.

b

c

e

Once again, please show all work and explain what you are doing (if necessary) for good rating. IF YOU COPY AND PASTE FROM ANOTHER SITE OR THIS ONE I WILL GIVE YOU 1 STAR REGARDLESS OF WHETHER IT IS CORRECT. Obviously I know how to use the internet too- that is not what I need. Thank you. :0)

Explanation / Answer

For 13, the two circles intersect when theta = pi/4. The rectangular coordinates are (3 sqrt(2), 3 sqrt(2)). For 15, it is only the circle 2 sin(theta) that figures into the area you want. Thus set up your integral with the 1/2 out front, limits of integration 0 to Pi/4 and the integrand of '4 sine squared theta.'. To integrate the sine squared function you need to use a trig trick - sine squared theta is 1/2 - 1/2 cos (2 theta). These are two easy integrals (be sure to manipulate the '1/2' in the second integral. For 20, the answer is the last one. Between 0 and Pi/4, you are subtracting away the area bounded by the petal curve. There are 8 repetitions of this as you move around the circle.

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