Grade 12 Polar Graphs Worksheet
A comprehensive worksheet for Grade 12 students covering polar coordinates, converting between polar and rectangular forms, and graphing polar equations.
Includes
Standards
Topics
Polar Graphs Worksheet
Name:
Date:
Score:
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?
x² + y² = 4x
x² + y² = 4y
x² = 4y
y² = 4x
5. Identify the type of curve represented by the polar equation r = 3 + 2cosθ.
Cardioid
Limacon with inner loop
Dimpled Limacon
Rose Curve
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.
True
False
9. The equation r = 5 represents a circle centered at the origin with radius 5.
True
False