A curve in polar coordinates is given by r115cos Point P is

A curve in polar coordinates is given by: r=11+5cos.
Point P is at =27pi/22.

a.) Find polar coordinate r for P, with r>0 and <<32.
r=

b.) Find cartesian coordinates for point P.
x=
y=

c.) How may times does the curve pass through the origin when 0<<2?
Answer:

Solution

A curve in polar coordinates is given by:
r = 11 + 5cos
P(r, ) = P(r, 27/22) = P(r, 27/22)

cos(27/22) = cos(+5/22) = -cos(5/22) =-cos(40 degree)

=-0.77

a)
r = 11 + 5cos = 12 + 5cos(27/22)
r = 11 +5(-0.77)

r=11 -3.85

r=7.15

P(r, ) = P(r, 27/22) = P[7.15, 27/22]
__________

b)
x = rcos = 7.15cos(40)=5.48
y = rsin =7.15sin(40)=4.6
x² + y² = r²
____________

c) Never
r = 11 + 5cos = 0
5cos = -11
cos = -2.2

No solution