Grade 12 Polar Graphs Worksheet

Polar Graphs Worksheet

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Plot the following polar coordinates on a polar grid:

a) (3, π/4)

b) (-2, 2π/3)

c) (4, -π/6)

d) (1, 3π/2)

2. Convert the rectangular coordinates (3, -3) to polar coordinates. Give your answer with r > 0 and 0 ≤ θ < 2π.

r =  

θ =  

3. Convert the polar coordinates (2, 5π/6) to rectangular coordinates.

x =  

y =  

4. Which of the following rectangular equations is equivalent to the polar equation r = 4sinθ?

5. Identify the type of curve represented by the polar equation r = 3 + 2cosθ.

6. Sketch the graph of the polar equation r = 2cos(3θ).

7. Sketch the graph of the polar equation r = 1 + sinθ.

8. The polar coordinates (r, θ) and (-r, θ + π) represent the same point.

9. The equation r = 5 represents a circle centered at the origin with radius 5.