APPC Polar Functions Review

Polar Coordinates

100

Find the exact rectangular coordinates for [-4, 5pi/3]

(-2, 2sqrt3)

200

Find another way to represent [3, pi/6] where r>0 and theta is between -2pi and 0. 

[3, -11pi/6]

300

Find another way to represent [2, 2pi/3] with r<0 and theta between 2pi and 4pi.

[-2, 11pi/3]

400

Find exact polar coordinates for (-4, -4).

[4sqrt2, 5pi/4] or [-4sqrt2, pi/4]

500

Find exact polar coordinates for (3, -sqrt3) where r<0. 

[-2sqrt3, 5pi/6]

Polar Equations

100

Convert 2x+3y=8 to a polar equation solved for r.

r=8/(2cos(theta)+3sin(theta))

200

Convert 4rcos(theta)+rsin(theta)=8 to a rectangular equation solved for y.

y = -4x+8 = 8-4x

300

Convert (x-6)²+y²=36 to a polar equation solved for r.

r=12cos(theta)

400

Convert r=3cos(theta) to a rectangular equation.

x²+y²=3x or x²-3x+y²=0

500

Convert r²sin(2theta)=-4 to a rectangular equation solved for y.

y=-2/x

Polar Graphs

100

Give 3 distinct points in polar coordinates that are on the graph of r = 1-2cos(theta)

(many possible answers)

[-1,0]  [1,pi/2]  [3,pi]  [1,3pi/2]

200

Sketch the graph of r = -4+4sin(theta)

(cardiod along positive vertical axis with maximum r=8)

300

Name a country outside the United States Miss Kehe has visited.

Australia, Canada, Cayman Islands, New Zealand

400

Give 3 distinct points in polar coordinates on the graph of r=-2sin(4theta)

(many possible answers)

[0,0]  [-2,pi/8]  [-sqrt(3),pi/6]  [sqrt(3),pi/3]  [2,3pi/8]

500

Sketch the graph of r = 3cos(5theta)

rose curve with 5 petals, symmetry on positive horizontal axis