Area of polar curves (NOT a test question)

Question

Find the point(s) of intersection for the polar curves with equations r = 3 sin θ and r = 2 − sin θ. (4 points)

	0, π

Thank you in advance.

Answer 1

pi/6, 5pi/6 are the angles of intersection

r = 3sin(theta) and r=2-sin(theta)

3sin(theta = 2-sin(theta)

4sin(theta) = 2

sin(theta) =2/4 = 1/2

theta = pi/6 or 5pi/6 or 30 or 150 degrees

the points of intersection are (3/4, 3sqr3/4) and (3/4, -3sqr3/4)

or (3/2, pi/6) and (3/2, 5pi/6)