1. Warm Up Calculator Active The curve given can be described by the equation r = θ + sin(2θ) for 0 < θ < π, where r is measured in meters and θ is measured in radians. 1) Find the area bounded by the curve and the x-axis. 2) Find the angle, θ, that corresponds to the point on the curve with x-coordinate -2. 3) For is negative. What does this fact say about r? What does it say about the curve?

2. Polar Curves Test Review

3. Change from a polar equation to a rectangular equation: Convert the rectangular equation to a polar equation: 3x + 2y – 1 = 0

4. Convert from polar to rectangular: Convert from rectangular to polar:

5. Graph (No calculator)

6. Write an equation for the graph.

7. Find three other polar coordinates where -2π <  < 2π for the point (2, -7π/6) (2, _____) (-2, _____) (-2, _____)

11. 1.Determine the arc length of the polar curve r = 2 + 2sinθ from θ = π/6 to θ = 5π/6 2) The area of the closed region bounded by the polar graph of is given by the integral

12. Find the slope of the curve r = 7 – 6sinθ at the point (7, π).

13. Find the value(s) of θ at which there are horizontal tangent lines on the graph of r = 1 + sinθ.

14. Calculator Active 1) Determine the area shared by the graphs of r = 1 + cos θ and r = 1 – cos θ 2) Determine the area outside r = but inside r = 2cos(2θ).